Syllabus for M.Sc. (Physics) Semester-I Mathematical ... · Syllabus for M.Sc. (Physics) Semester-I...

Syllabus for M.Sc. (Physics) Semester-I

Mathematical Physics

Paper Code : PHM-1001

M.M: 100 Credits : 04

Lectures: 48

Tutorials: 08

UNIT-I: Review of Tensors Analysis and General Relativity

Tensor Algebra: Linear combinations, direct product, contraction, tensor densities, transformation of

affine connection, covariant differentiation, gradient, curl and divergence.

UNIT-II: Green’s Functions

Introduction to Green’s function method, Green’s function as a solution to Poisson’s equation with a point

source, symmetry of Green’s function, forms of Green’s functions, spherical polar coordinate expansion,

quantum mechanical scattering-Neuman series as well as Green’s function solutions, eigen function

expansion, one dimensional case, integral-differential equation, linear Harmonic oscillator, Green’s

function and Dirac delta function.

Unit-III: Group Theory I

Symmetries in classical and Quantum mechanics, Definition and examples of groups, Cyclic groups,

Subgroups, Conjugacy classes, Invariant subgroups, Cosets and Factor groups, Homomorphism,

Isomorphism, group representation, Schur’s Lemma, Orthogonality of characters, Permutation group NS ,

Partition and Young Diagram. Point groups in the context of crystals and molecules.

Unit-IV: Group Theory II

Continuous groups, Definition and example of Lie groups and Lie Algebras, Rotation groups SO(2),

SO(3) and their irreducible representations, Angular momentum algebra,

Rotation group SO(n). Connection between SU(2) and SO(3). Spin and Iso-spin groups,

Group SU(3), Unitary group SU(n), Many-particle Irreducible representation, Young diagrams for Unitary

groups and their simple application for SU(2) and SU(3).

Books Recommended:

1. Steven Weinberg : Gravitation and Cosmology (John Wiley)

2. Arfken G. B. : Mathematical Methods for Physicist (Academic Press)

Third Edition)

3. Joshi A. W.. : Elements of Group theory for physicist (New Age)

4. Tung W. K. : Group theory in Physics (world Scientific)


Classical Mechanics


M.M. : 100 Credits: 04

Lectures: 48

Tutorials: 08

Unit-I: Lagrangian & Hamiltonian Dynamics

Review of variational calculus and Euler-Lagrange equations. Hamilton’s equations from principle of least

action. Equations of canonical transformations, properties of four special type of canonical

transformations, harmonic oscillator. Poisson bracket and its properties, equation of motion, infinititesimal

canonical transformation, conservations theorems in P.B. formalism. Invariance of P.B. under canonical

transformations.

Unit-II: Hamilton-Jacobi Theory and Rigid Body Motion-I

Hamilton-Jacobi equation for Hamilton’s principal and characteristic functions, harmonic oscillator,

Noether’s theorem, action angle variables, frequency of harmonic oscillator, Kepler’s problem in action-

angle variables.

Rigid Body Motion: Degrees of freedom, orthogonal transformations, statements of Euler’s and Chasle’s

theorems, infinitesimal rotations, rotating coordinate systems, centrifugal and Coriolis force. Angular

momentum and kinetic energy of a rigid body.

Unit-III: Rigid Body Motion-II and Small Oscillations

Inertia tensor, principal axes transformation Euler’s equation of motion for a rigid body, torque free

motion of symmetric top, precession of Earth’s axis of rotation and a charged particle in magnetic field.

Small Oscillations: General formalism, eigenvalue equation, normal coordinates and normal modes.

Unit-IV: Continuous Media, Perturbation Theory and Chaos

Continuous Media: Coupled pendula, triatomic molecule, Linear chain of interacting particles, elastic rod

problem, Lagrangian formalism, stress energy tensor.

Classical Perturbation Theory: Time dependent perturbation theory, harmonic oscillator.

Qualitative discussion of Classical Choas, Phase space dynamics and stability analysis.

Books Recommended:

1. Goldstein, H, Poole, C. and

Safko, J.

: Classical Mechanics, 3rd

Edition (Pearson)

2. Rana, N.C. and Joag, P.S. : Classical Mechanics (Tata McGraw-Hill)


Quantum Mechanics-I


M.M.: 100 Credit: 04

Lectures: 48

Tutorials: 08 UNIT-I: Matrix Formulation of Quantum Mechanics.

Linear vector spaces, elements of Hilbert space, Dirac’s bra-ket notation, triangle inequality, Schwartz inequality

and Gram-Schmidt theorem, linear operators, projection operator, Hermitian and unitary operators, matrix

representation of operators, elements of transformation theory, linear harmonic oscillator by operator method.

Time development of a quantum mechanical system: Schrödinger, Heisenberg and interaction pictures,

Heisenberg’s equation of motion.

Problems based on the above topics (Shankar)

UNIT-II: Approximation Methods.

Time-independent perturbation theory

Nondegenerate perturbation theory: General formulation, First order theory, Second-order energies.

Degenerate perturbation theory: Two-fold degeneracy, Higher-order degeneracy.

Application of the perturbation theory: Harmonic perturbation of a harmonic oscillator, Harmonic oscillator with linear perturbation, The fine structure of hydrogen, The relativistic correction, Spin-Orbit coupling, The Zeeman effect,

Hyperfine splitting, Van der Waals interaction, Stark effect. The variational principle: Theory and its application to find out the ground state energies of harmonic oscillator and

helium atom.

Time Dependent perturbation theory: General formulation, sinusoidal perturbations, Emission and absorption of radiation, Fermi's golden rule.

UNIT-III: Collision Theory

Definition of S- and T- matrices, the Lippmann-Schwinger equation, Derivation for the scattering amplitude,

Optical theorm (first and higher order), Born approximation, Scattering from Yukawa and screened coulomb

potentials, Low-energy soft-sphere scattering, , Eikonal approximation, Method of partial waves, unitarity and

phase shifts, determination of phase shifts, hard sphere scattering, scattering from square well potential, Low-energy

scattering and bound states, Resonance scattering, Breit-Wigner formula.

UNIT-IV: Symmetries in Quantum Mechanics

Space and time displacements, displacement operators, symmetry and degeneracy, rotation operator, orbital angular

momentum operators and their commutation relations, eigen values and eigen functions of L2 and Lz operators, spin

angular momentum operators and their algebra; Eigen states of spin -2

1, 1,

2

3particles, total angular momentum J ,

coupling of two angular momenta, Clebsch-Gordan Coefficients and their properties, Wigner-Eckart theorem

(statement and Explanation).

Books Recommended:

1. L. I. Schiff. : Quantum Mechanics, 3rd

Ed. (McGraw Hill) 2. R. Shankar : Principles of Quantum Mechanics (Plenum) 3. J. J. Sakurai : Modern Quantum Mechanics (Rev. Ed.,Addison-Wesley) 4. David J. Griffiths : Introduction to Quantum Mechanics (2

nd Ed.,Pearson)

5. N. Zettili : Quantum Mechanics: Concepts and Applications (2nd

Ed.,Wiley)


Electronics



Lectures: 48

Tutorials: 08

UNIT-I: Codes, Basic and Combinational Logic Circuits

BCD, ASCII and Gray Codes. Basics logic gates, logic systems, laws and theorems of Boolean algebra.

Different ways of implementing exclusive-OR gate, TTL and CMOS logic family characteristics. Open

collector TTL gates, tri-state gates. Sum of product and product of sum representation. Algebraic and

Karnaugh map simplifications. binary adders, digital (magnitude) comparators, parity checker/generator.

Decoders/demultiplexers, data selectors/multiplexers. Encoders Read only memory (ROM), ROM

organization and applications, PROMS, EPROMS, PAL and PLA.

UNIT-II : Sequential Logic Circuits and Very Large Scale Integrated System

Clocked S-R flip-flops, J-K and D-type flip-flops, edge triggering, preset and clear inputs. Ripple

counters, synchronous binary counters, decade counters, shift registers, shift and ring counters, up/down

counters. Static and dynamic random access memory (RAM), Microprocessors and Microcontroller

basics.

UNIT-III : Operational Amplifier Applications and Regulators

OP Amp, ideal characteristics, op amp as inverting amplifier, effect of finite open loop gain, generalized

basic equation of op amp with impedances, integrator and differentiator, inverting and non-inverting

summer, voltage follower. Op Amp parameters, offset voltage and current, slew rate, full wave BW,

CMRR. OP AMP as voltage regulator, fixed and variable 3 pin regulator, switching regulator.

UNIT-IV : Waveform Generators, Waveshaping and Data Conversion

Barkhausen criterion of oscillation. Wein’s bridge and LC oscillators (op amp). Comparators, regenerative

comparator (Schmitt trigger), square and triangular wave generator, voltage controlled generators.

Multivibrators: astable/monostable and 555 timer. D-A converters: weighted resistor, ladder and

multiplying types. A-D converters: parallel, counter type, successive approximation and dual slope

integration types.

Books Recommended:

1. Millman, J. and Grabel, A. : Microelectronics; Digital Analog Circuits and Systems (Tata McGraw Hill)

2. Leach, D.P. and Malvino, A.P. : Digital Principles and Applications (Tata McGraw Hill) 3. Sedra, A.S. and Smith, K.C. : Microelectronics Circuits (Oxford University Press) 4. Tocci, R.J. and Widmer, N.S. : Digital Systems, Principles and Applications (Prentice Hall) 5. Moris Mano, M. : Digital Design (Pearson)


Experimental Techniques


Credits: 02

Lectures: 24

Tutorials: 04

UNIT-I: Spectroscopic Techniques.

Light sources, Prism and grating spectrographs, Grating mountings: Czerny-Turner and Ebert mountings,

Monochromators. Resolution and dispersion of prism and grating spectrographs. Light detectors:

Photomultiplier, charged coupled device (CCD).

UNIT-II: Continuum sources for absorption studies: uv, visible and infrared sources, Single-beam and double-

beam infrared instruments, infrared detectors. Basic of Electron spin resonance (ESR) and Nuclear magnetic

resonance (NMR), Chemical shift.

UNIT-III: Nuclear Instrumentations

Detectors: Ionization chamber, proportional counter, GM counter, scintillation detectors, solid state detectors,

surface barrier and HPGe detectors. Time of flight technique. Idea of coincidence measurements.

Determination of lifetime of nuclear levels.

UNIT-IV: Data Analysis and Vacuum Techniques

Data interpretation and analysis; Precision and accuracy, error analysis, propagation of errors, least

squares fitting, linear and nonlinear curve fitting, chi-square test; Error analysis. Propagation of error. Plotting of Graphs. Least square fitting.

Vacuum Techniques: Basis idea of conductance, pumping speed, mechanical pump, diffusion pump.

Gauges: Penning and Pirani.

Books Recommended:

1. Thorne, A., Litzen, U,

Johansson, S

: Spectrophysics (Springer)

2. Banwell, C.S. : Fundamental of Molecular Spectroscopy (Tata

McGrawHill)

3. Sawyer, R.A. : Experimental Spectroscopy (Dover)

4. Aruldhas, G. : Molecular Structure and Spectroscopy (Printice Hall of

India)

5. Leo, W.R. : Techniques for Nuclear and Particle Physics Experiments

(Narosa)

6. Kapoor, S.S. &

Ramamurthy, V.S.

: Nuclear Radiation Detectors (New Age)

7. Singru, R.M. : Introduction to Experimental Nuclear Physics (Wiley

Eastern Pvt.) 8. Long, D.A. Raman Spectroscopy (McGraw Hill, New York

M.Sc. (Physics) I Semester

Lab-I : General Lab.


1. (a) To find out the magnetic susceptibility of FeCl3 solution of given strength.

(b) To find out the magnetic moment of Fe3+

.

2. To determine the wavelength of the sodium D lines and the wavelength difference between D1 and D2

lines using Michelson Interferometer.

3. (a) To measure the wave length of He-Ne LASER, light with verniar caliper.

(b) To measure the wavelength of He-Ne LASER using diffraction grating.

4. To study the percentage regulation of a solid state power supply at different load regulations.

(a) after filter (b) after zener diode

(c) after transistor state (d) after OPAMP (741)

5. To study the frequency response of RC coupled CE transistor amplifier (i) with and (ii) without

feedback.

6. (i) To draw transfer characteristics of OP AMP (741) in inverting mode in closed loop.

(ii) To determine CMRR and offset voltage of an OPAMP (741).

7. To study variation of the amplitude modulation index with input frequency and input voltage with the

help of CRO. To plot input modulating voltage and detected output voltage.

8. To study Wein’s bridge oscillator using OPAMP (741) and measure its frequency (range approx.

100Hz to 50 KHz). Also determine its output resistance at two different frequencies.

9. To record the arc spectrum of copper with the help of a medium quartz spectrograph and verify the

Hartmann formula.

10. To determine the refractive index of air using Jamin’s Interferometer.

11. To study the directional characteristics (directional pattern) of a Microwave Horn at

different distances.

12. (a) To determine the absorption co-efficient of a transparent material (glass slide).

(b) To verify Malus Law

13. To determine the verdit’s constant of material for a given wavelength of light.

(Faraday’s) effect.

14. Measurement of Plasma Paramenters (floating potential, Plasma Potential, electron Temperature and ion density) by Langmuir Probe.

------------------------------------------------------------------------------------------------------------

*Minor alteration in the objects of the experiment and any addition/deletion may be done by Incharge of

the Lab. and Chairman.

Syllabus for M.Sc. (Physics) Semester-II

Classical Electrodynamics (PHM-2001)

M.M.:100 Credits: 04

Lectures: 48

Tutorials: 08

Unit-I : Electromagnetic Waves-I

Review of Maxwell’s equation. The Maxwell stress tensor, Radiation pressure, Propagation of e.m.

waves in non-conducting medium. Propagation of e.m. waves in a conducting medium. Skin depth.

Linear, circular and elliptical polarization. Oblique incidence – The Fresnel Equations, Total internal

reflection, Brewster’s angle.

Unit-II : Electromagnetic Waves-II

Reflection and refraction from a metallic surface. Propagation of waves between perfectly conducting

planes. Waves in hollow conductors. T.E. and T.M. modes. Rectangular wave guides (TE and TM

cases). Resonant cavities.

Unit-III : Electromagnetic Radiation

Lienard-Weichert potentials. Fields produced by charged particles in motion. Radiation from

accelerated charged particles-Larmor’s formula and its relativistic generalization. Scattering of e.m.

radiation by free charges. Thomson scattering. Scattering by a system of charges, dipole radiation.

Dispersion relations in plasma.

Unit-IV : Interference and Diffraction of e.m. Waves

Interference: Interference of two coherent beams. Visibility and resolution of interference fringes.

Scalar Diffraction Theory: Helmholtz-Kirchhoff’s integral and Kirchhoff’s diffraction theory. Fresnel

and Fraunhofer diffraction. Fraunhofer diffraction by a single slit and double slit. Fresnel diffraction

by a straight edge.

Books Recommended:

1. Marion, J.B. : Classical Electromagnetic Radiation (Academic Press)

2. Jackson, J.D. : Classical Electrodynamics (John Wiley)

3. Laud, B.B. : Electromagnetics (Wiley Eastern)

Syllabus for M.Sc. (Physics) Semester-II Atomic, Molecular and Laser Physics (PHM-2002)

Credits: 04

Lectures: 48

Tutorials: 08

Unit I: Atomic Spectroscopy

Quantum states of an electron in an atom. LS and JJ coupling schemes. Terms for equivalent and non-equivalent

electron atom. Spectra of one electron systems. Qualitative idea of the following: Electron spin, spin orbit

interaction, fine structure, relativity correction and radiation correction (Lamb Shift). Electric dipole selection

rules. Intensity rules.

Penetrating and non-penetrating orbits, quantum defect. Alkali type spectra. Spectrum of helium. Normal and

anomalous Zeeman effect. Paschen-Back effect. Stark effect. Hyperfine structure and isotopic shifts. X-rays

and Auger transitions.

Unit II: Molecular Spectroscopy

Born-Oppenheimer approximation. Rotational spectra of diatomic molecules. Vibrational spectra of diatomic

molecules. Rotation- Vibration spectra of diatomic molecules. Electronic spectra of diatomic molecules.

Hund’s cases. Vibrational structure of electronic transition. Selection rules. Rotational fine structure: 1 -1

transition. Franck-Condon principle. Intensity of bands in absorption and emission. Isotopic effect. Infrared

and Raman spectra of linear molecules.

Unit III: Laser Physics

Absorption, spontaneous and stimulated emission. Einstein coefficients, Trasition propability and lifetime of

an atom in an excited state. Population inversion. Laser rate equations: The three level and four level systems.

Line broadening mechanism. Shape and width of spectral lines. Optical resonators: Quality factor. Losses

inside the cavity. Threshold conditions. Schawlow-Townes condition. Transverse and longitudinal mode

selection.

Unit IV: Laser Systems

He-Ne laser. CO2 laser. Four level solid state lasers. Dye lasers. Ar+ laser. Excimer lasers. Properties of laser

beam: directionality, monochromacity, intensity, coherence (temporal and Spatial). Applications of lasers:

Laser induced fusion. Isotope separation.

Books recommended:

1. White, H.E.

2. Bransden B.H. and Joachain C J

: Introduction to Atomic Spectra (McGraw Hill)

:Physics of Atoms and Molecules( Pearson)

2. King, G.W. : Spectroscopy and Molecular Structure (Rinehart

and

Winston)

3. Herzberg, G. : Spectra of Diatomic Molecules (D. Van

Nostrand)

4. Thyagarayan, K. and Ghatak, A.K. : LASERS: Theory & Application

5. Laud, B.B. : Laser and Non-linear Optics (Wetey-Eastern)

Syllabus for M.Sc. (Physics) Semester-II

Nuclear and Particle Physics (PHM-2003)

M. M.: 100 Credits: 04

Lectures: 48

Tutorials: 08

Unit I - Nuclear Decay :

Alpha decay; energetics of -decay, Geizer-Nuttal law, Gamow theory of -decay. Beta decay:

Neutrino hypothesis, energetics of -decay, Fermi theory of -decay, Fermi-Kurie plot, comparative half

life. Selection rules: allowed and forbidden transitions, Idea of electron capture, Gamma decay: energetic

of -decay, Multipole radiations, Selection rules, Idea of Internal Conversion of -rays and Coulomb excitation.

Unit II – Nuclear Reactions:

Kinds of nuclear reactions, energetics of nuclear reactions, standard Q-equation and its solution,

nuclear reaction, cross-section, idea of differential cross-section, compound reaction mechanism and its

verification – Ghoshal’s experiment, Idea of pre-compound emission, direct reactions and their signatures.

Liquid drop model: Weizsacker’s semi-empirical mass formula and some of its applications.

Unit-III

Neutral units, Review of Particle Accelerations and Detectors, Linacs, Synchrotrons and colliding-beam

accelerators, principle of Cerenkov counters and calorimeters.

The fundamental fermions and interactions. Classification of particles into – fermions and bosons, leptons and

hadrons, particles and resonant states.

Space reflection and parity, parity of charged pion, parity non-conservation in -decay, charge conjugation, time

reversal, CPT theorem, symmetry and conservation rules.

Neutrino flavours, mass limits, neutrino detection helicity of neutrino, energy of neutrino for pion decay in flight

and decay at rest, difference between v and v and ve and v and neutrino flavour oscillations.

Unit-IV

Introduction to Spin ½ and Spin 3/2 Resonances, Quark model of hadrons, quark flavours, confinement and QCD

potential. Isospin and Gell-Mann-Nishijima relation. Baryon decuplet and octet. Colour degree of freedom.

Magnetic moments of baryons, Mass relations and splittings. Mesons built of light and heavy quarks.

Weak, electromagnetic and strong decays of particles, calculation of branching ratios, weak decays of strange

particles and Cabbibo theory. Decay rates for )( and )( eee processes.

Regeneration phenomenon, strangeness oscillations, KL—KS mass difference and CP non-conservation in K0 –

decays.

Books Recommended:

1. Enge, H.A. : Introduction to Nuclear Physics (Addison Wesley)

2. Preston, M.A. & Bhaduri, R. : Nuclear Physics (Addison Wesley)

3. Roy, R.R. & Nigam, B.P. : Nuclear Physics (John Wiley)

4. Evans, R.D. : Atomic Nucleus (McGraw Hill)

5. Halliday, D. : Introductory Nuclear Physics (John Wiley)

6. Ghosal, S.N. : Atomic and Nuclear Physics (S. Chand & Company Ltd.)

6. Segre, E. : Nuclei and Particles (2nd

Ed.) (Benjamin/Cummings)

7. Hughes, I.S. : Elementary Particles (Cambridge)

8. Perkins, D.H. : Introduction to High Energy Physics (Addison Wesley)

9. Povh. Rith. Scholz Zetche : Particles and Nuclei (Springer)

Syllabus for M.Sc. (Physics) Semester II

Condensed Matter Physics (PHM-2004)

Max. Marks:100 Credits: 02

Lectures: 24

Tutorials: 04

UNIT –I

Symmetry Elements: Symmetry operations, proper rotation axis, improper rotation axis, rotoreflection,

rotoinversion, glide planes, screw axes.

Symmetry Groups: Point groups, space groups; Quasi crystals.

Imperfections: Types of imperfections: Point defects (Schottky and Frenkel), Dislocations, Illustration of

types of dislocation, Burger’s vector, Low angle grain boundaries.

UNIT –II

Reciprocal Lattice: Concept of Brillouin zone; reciprocal lattice, its significance, relationships between

direct and reciprocal primitive translation vectors. Construction of reciprocal lattices; determination of

reciprocal lattice of SC, BCC, FCC.

Diffraction from Crystals and Crystal Structure Study: Bragg diffraction, Bragg formulation, Laue formulation, Fourier analysis, Structure factor of BCC, FCC,

diamond and Polyatomic lattice.

UNIT-III

Free Electron Fermi Gas: Review of Sommerfeld model of free election gas; Boltzmann transport

equation, derivation of the expression for d.c. conductivity.

Energy Bands: Electron wave equation in periodic crystal potential, solution for energy at zone boundary,

comparative picture of the band structures of metals, semi-metals and insulators.

Semiconductors: Band gap, concept of hole; equations of motion of charge carriers in electric and

magnetic fields, effective mass, intrinsic and extrinsic conductivity, law of mass action.

UNIT –IV

Magnetism: Origin of magnetism. Quantum theory of diamagnetism and paramagnetism. Curie law.

Superconductivity: Occurrence of superconductivity, Meissner effect, London equation, effect of magnetic

field, type I & type II superconductors. Cooper pairs and elementary discussion of BCS model.

Books Recommended:

1. Kittel, C. : Introduction to Solid State Physics, 8th

Ed. (John-Wiley)

2. Srivastava, J.P. : Elements of Solid State Physics (Prentice-Hall of India)

3. Wahab, M.A. : Solid State Physics: Structure and Properties of Materials (Alpha

Science International Ltd.)

4. Ali Omar, M. : Elementary Solid State Physics : Principles and Applications

(Addison-Wesley Professional).

Syllabus for M.Sc. (Physics) Semester II

Astrophysics (PHM-2005)

Credits: 02

Lectures: 24

Tutorials : 04

Unit-I

Photometric Concepts(Intensity, Radiation and Luminosity). Stellar Magnitudes (Apparent, Absolute,

Photographic, Visual and Bolometric) and Colour Indices. Recapitulation of Radiation Mechanisms.

Emission & Absorption Coefficients and Optical Thickness. Radiative Transfer Equation in an atmosphere

and its Simple Applications

Unit-II

Virial Theorem & its Applications. Boltmann & Saha Ionization Formula and its Applications in Spectral

Classification (Harvard and Yerkes). H-R Diagrams. Equation of Stellar Structure (Hydrostatic

Equilibrium, Mass &Temperature Distribution and Energy Transport in Stellar Interiors) and Physical

State of the gas.

Unit-III

Stellar Energy Sources and Nucleosynthesis [Basic Conditions, Thermonuclear Reaction Rates and

Nuclear Burning (P-P, CNO, Triple Alpha, Carbon & Other Heavy Elements)], Internal Structure of the

Sun and Solar Neutrino Problem.

Unit-IV

Various Era of the Evolution of Universe ( Hadron Era, Lepton Era, Radiation Era, Matter Era and

Formation of the Galaxies). Cosmological Observations (Huble Law, Hubble Constant, Age of the

Universe, Redshift, Microwave Background Radiation, Isotropy of the Matter & Radiation and Relative

Helium Abundance).

Books Recommended:

1. The New Cosmos: Albrecht Unsold and Bodo Baschek (Springer-Verlag)

2. Fundamentals of Astronomy: H. Karttunen, P. Kroger, H. Oja, M.Poutanen and

K.J. Donner (Springer-Verlag)

3. Stellar Structure and Evolution: R. Kippenhahn and A. Weigert (Springer-Verlag)

4. Text Book of Astronomy and Astrophysics with Elements of Cosmology:

V.B. Bhatia (Narosa Publishing House).

5. Stellar Evolution and Nucleosynthesis (Cambridge): S.G. Ryan and A.J. Norton

M.Sc. (Physics) II Semester

PHM-C Lab.

MM: 100 Credits: 6

1. To determine Hall coefficient and mobility of charge carrier in a given sample of semiconductor.

2. To measure wavelengths of the Balmer lines of Hydrogen spectrum and to determine the

Rydberg constant for Hydrogen atom from the measurement of these lines.

3. To determine the numerical aperture and bending loss in the given optical fiber.

4. To study monostable multivibrator using timer IC 555 and to measure its pulse width. (Range

approx. 50 sec. to 1m sec.).

5. To study second order active low pass & high pass Butter worth filter and plot the frequency

response curve and find its cut-off frequency and attenuation factor.

6. To study d.c. transfer characteristics of TTL and CMOS inverter (Using IC’s 7400 & 4011).

Also study input and output characteristics of TTL inverter.

7. To study triangular wave generator using 741 based Schmitt trigger and integrating circuit. Also

study its duty cycles modulation.

8. To study D/A converter using (i) 4-bit binary ladder network and (ii) an 8-bit IC 1408.

9. To analyze the given I2 absorption spectrum.

10. To determine the wavelength () of sodium light and d of D1 and D2 lines by Febry Perot

interferometer.

11. To find out speed of light with the help of optical fiber etc.

12. To Pspice simulate the common emitter RC coupled BJT amplifier circuits and study variation

of gain and f1 with RC and variation of f1 with CC with feedback and without feedback cases.

13. To measure capacitance using OP-AMP (IC741).

14. To determine the Ionization Potential of Argon.

------------------------------------------------------------------------------------------------------------

Minor alteration in the objects of the experiment and any addition/deletion may be done by Incharge of the

Lab. and Chairman.

Syllabus for M.Sc. (Physics) Semester-III

Quantum Mechanics-II

Paper Code : PHM3001


Lectures: 48

Tutorials: 08

UNIT-I: Relativistic Wave Equation

Relativity and problems will Schrodinger equation, Free particle Klein-Fock-Gordon equation and

physical problems associated with it, continuity equation, minimal electromagnetic coupling, non-

relativistic reduction.

Dirac equation, Covariant and adjoint Dirac equations, continuity equation, free-particle solution, Dirac

and Feynman interpretations of negative energy states, Dirac equation in electromagnetic field, non-

relativistic reduction.

UNIT-II: Dirac Equation in a Central Field, spin-orbit energy, spin angular momentum, constants of

motion for central field and their simultaneous eigen-functions, energy levels of relativistic hydrogen

atom, anomalous magnetic moment.

Unit-III: Quantization of Klein-Gordon and Dirac field

Lagrangian field theory. Statement of Noether’s theorem and conserved energy momentum tensor.

Quantization of Klein-Gordon field (number representation), Hermitian and non-Hermitian fields energy,

momentum and charged operators for scalar fields. Covariant commutation rules and meson propagator.

Quantization of Dirac field (number representation), Covariant commutation rules and the fermion

propagator.

Unit-IV: Quantization of e.m. field

Covariant quantization of e.m. field. Four polarization vector. Covariant commutation rules and the

photon propagator.

QED Lagrangian. The S-matrix expansion. Statement of Wick’s theorem. Feynman diagrams in

configuration space. Scattering from an external field.

Books Recommended:

1. Biswas, S.N. : Quantum Mechanics; Chapters 8 & 9

(Books and Allied )

2. Schiff, L.I. : Quantum Mechanics, Chapters 13,14

(McGraw Hill; 3rd

Edition)

3. Bjorken, J.D. and

Drell, S.D.

: Relativistic Quantum Mechanics;

Chapters 1 and 3 (McGraw Hill)

4. Mandl, F. and Shaw,

G.

: Quantum Field Theory (John-Wiley)

5. Sakurai, J.J. : Advanced Quantum Mechanics (Benjamin/Cummings)


Statistical Physics


M.M.: 100 Credit: 04

Lectures: 48

Tutorials: 08

Unit-I:

Introduction to statistical physics, phase space and phase space trajectory, concept of statistical ensemble,

distribution function, mean value of a physical quantity, statistical equilibrium, statistical independence

and quasi-closed systems. Fluctuations and its dependence on number of particles.

Liouville’s theorem and its significance, microcanonical distribution in classical statistics, statistical

matrix, statistical distribution in quantum statistics.

Entropy. Law of increase of entropy. Thermodynamic quantities: temperature, pressure, free energy and

thermodynamic potential. Theorem of small increments (no derivation), Concept of chemical potential,

dependence of thermodynamic quantities on number of particles. An ideal gas in microcanonical

ensemble.

Unit-II:

Gibbs canonical distribution. The Maxwellian distribution. Free energy and partition function.

Grand canonical distribution and partition function. Ideal gas in canonical and grand canonical ensemble.

Energy fluctuations in canonical and concentration fluctuations in grand canonical ensemble.

Boltzmann distribution. The Boltzmann distribution in classical statistics. Free energy and equation of

state of an ideal gas. Chemical potential of a monatomic ideal gas.

Unit-III:

F-D and B-E distributions. Equation of state of ideal F-D and B-E gases of elementary particles.

Degenerate electron gas, equation of state, degeneracy temperature, specific heat. The electron gas in

metals, Richardson effect.

Degenerate Bose gas – Bose-Einstein condensation, condensation temperature, specific heat, entropy and

pressure.

Black-body radiation: Planck’s formula and Boltzmann’s law.

Magnetism of an electron gas – Pauli paramagnetism, Landau diamagnetism, de-Hass Van Alphen effect.

Unit-IV:

Ferromagnetism – First and second order phase transition, the Bragg-Williams approximation, Heisenberg

and Ising model in one dimension; an idea in two dimensions.

Fluctuations : The Gaussian distribution for one and more than one variable. Fluctuations in

thermodynamic qualities. Fluctuations in ideal gas. Poisson’s formula. Energy fluctuations in canonical

and concentration fluctuations in grand canonical ensemble – application to perfect classical/quantum gas.

Random Walk and Brownian motion, introduction to non-equilibrium process.

Books Recommended:

1. Landau, L.D. and

Lifshitz, E.M : Statistical Physics (3rd Edition) Vol. V, Part-I (Pergamon Press)

2. Pathria, R.K. : Statistical Mechanics (Butterworth-Heinemann) 3. W. Greiner,

Ludwig Neise & Horst Stoecker

: Thermodynamics and Statistical Mechanics (Springer)

4. Yu. B. Rumer &

M. Sh. Rajvkin Thermodynamics, Statistical Physics, and Kinematics (Mir Publisher, Moscow)


Atomic and Laser Spectroscopy

Paper Code : PHM3012 Credits:04

Lectures: 48

Tutorials: 08

Unit-I: Atomic Structure

Complex Spectra: Vector model for three or more valence electrons. Scandium and oxygen spectra. Inverted terms.

Compound doublet. Series perturbation, nature and conditions for term perturbations, anomalous principal series in

copper and diffuse series in cadmium. Inner-Shell Excitation and Autoionization, autoionization in calcium. Line

intensities, Transition probabilities, oscillator strength and sum rules. Forbidden transitions (M1, M2 and E2).

Unit-II: The Analysis of Atomic Spectra

Observations, Recording of spectrum on high resolution grating spectrograph. Triggered Spark source. Wavelength

calibration using a polynomial fit. Predictions : Semi-empirical Relations, Ab Initio Theoretical predictions

(Qaulitative), Parametric predictions. Isoelectronic Sequences and Highly Charged Ions, Term Analysis in Practice.

Beam-Foil Spectroscopy. Time delayed Spectroscopy. Inter-combination transitions. Lifetime measurement of the

excited states using Beam-Foil technique. Precision lifetime measurements in fast beam with lasers. Determination

of the Ionization Energy (I.P.)

Unit-III: Laser Spectroscopy

Laser as spectroscopic light sources. Absorption spectroscopy with lasers. Frequency modulation, photoacaustic,

optogalvanic and ionization spectroscopy. Laser induced fluorescence. Optical pumping. Double Resonance

Methods: Optical-RF and optical-optical double resonance. Stepwise excitation, characteristic properties of Rydberg

atoms, spectroscopy of Rydberg states.

Unit-IV: Non-Linear and Molecular Beam Laser Spectroscopy

Hole burning, Lamb dip, Saturation spectroscopy. Polarization spectroscopy. Two-photon absorption. Multiphoton

spectroscopy. Molecular Beam: Reduction of Doppler widths, sub-Doppler spectroscopy in collimated

molecular beam.

Books Recommended:

1.

White, HE

: Introduction to Atomic Spectra (McGraw-Hill)

2. A.Thorne,U.Litzen

and S. Johansson

: Spectrophysics: Principles and Applications

3. Kuhn, HC : Atomic Spectra (Longman)

4. Demtroder, W : Laser Spectroscopy (Springer Verlag)

5. Hollas, JM : High Resolution Spectroscopy (John Wiley)


Condensed Matter Physics –A



Lectures: 48

Tutorials: 08

Unit-I:

Review of the concept of reciprocal lattice, Properties of reciprocal lattice, reciprocal lattice of a hexagonal space

lattice, calculation of structure factor for FCC and hexagonal crystals.

Lattice Vibrations: Adiabatic approximation. General Theory of harmonic approximation for a three-dimensional

crystal, normal modes of real crystals, dispersion curve. Theory of neutron-phonon scattering, the determination of

vibration spectra by inelastic neutron scattering, experimental set up.

Unit-II:

Plasmons, Polaritons: Plasma oscillations, plasmons. Transverse optical modes in plasma, application to optical

phonon modes in ionic crystals, interaction of e.m. waves with optical modes (polaritons). LST relation.

Thermal Properties: Classical lattice heat capacity, quantum theory of lattice heat capacity (Einstein model; Phonon

density of states, Debye continuum model). Electron heat capacity.

Anharmonic effects, thermal expansion, phonon collision processes, occurrence of thermal resistance, phonon

thermal conductivity, temperature dependence, influence of isotope scattering, size effect.

Unit-III

Electron Energy Bands: Failure of free electron model (a review). Periodicity of Bloch functions and their eigen

values, zone schemes. Tight binding approximation, Wigner-Seitz cellular method.

Fermi Surface: Construction of Fermi surface. Electrons in a uniform magnetic field, Onsager quantization

condition. Experimental methods of studying Fermi surface (Cyclotron resonance, de Haas van Alphen effect),

closed and open orbits.

Unit-IV:

Magnetotransport: Classical theory of mgnetoconductivity, a.c. conductivity of metals. Boltzmann equation in the

magnetic field, Hall effect, magnetoresistance in two-band model.

Magnetism: Quantum theory of magnetic susceptibility, van Vleck paramagnetism, Pauli paramagnetism.

Temperature dependence of spontaneous magnetization. Exchange interaction (two electron system), Heisenberg

model (spin Hamiltonian). Ferromagnetic domains. Anisotropy energy, Bloch wall.

Books Recommended:

1. Kittel, C. : Introduction to Solid State Physics 8th

Ed. (John Wiley) 2. Srivastava, J.P. : Elements of Solid State Physics (Prentice-Hall) 3. Ziman, J.M. : Principles of the Theory of Solids (Vikas) 4. Animalu,

A.O.E. : Intermediate Quantum Theory of Crystalline Solids (Prentice-Hall)

(BOS: 30.5.2017)

Syllabus for M.Sc. III Semester

High Energy Physics –A

Paper Code: PHM3021

M.M.: 100 Credits: 04

Lectures: 48

Tutorials: 08

Unit-I: Relativistic Kinematics

Review of Lorentz transformations for energy and momentum, four-vectors and invariants, Laboratory

and Centre-of-momentum systems, calculation of energy, momentum and angle of particles produced in

nuclear reactions in Lab. and centre-of-momentum frames and their transformations and calculation of

threshold energies for particle production.

Mandelstam variables, Fermi Golden Rule, differential and total scattering cross sections, Lorentz

invariant phase space, calculation of decay rates and phase space for two- and three-body decays, Dalitz

plots and their applications to three-body decays.

Unit-II: High Energy Hadron-Nucleon and Hadron-Nucleus Interactions.

High energy hadron-nucleon collisions: Features of relativistic hadron-nucleon collisions upto very high

energy, behaviour of elastic, inelastic and total cross-sections as a function of incident energy, multiplicity

distribution, Negative Binomial Distribution, KNO scaling and Feynman scaling.

Relativistic hadron-nucleus and ion-ion collisions: Rapidity and pseudorapidity variables. Lab. and CM-

rapidity, Maximum and minimum rapidities, Pseudorapidity distribution in projectile, target and central

fragmentation regions..

Fluctuations and correlations: Two-particle correlations, short- and long-range multiplicity correlations,

particle correlation and clusterization, Multiplicity fluctuations, Entropy and its generalization; Shanon

and Renyi entropies.

Features of non-statistical fluctuations: Intermittency and beyond-; erraticity, Multifractality and

multifractal specific heat.

Unit-III: Ultra-relativistic Nucleus-Nucleus Collisions, QGP formation and its Signatures.

Ultra-relativistic nucleus-nucleus collisions: Glauber model of nucleus-nucleus collision, participant-

spectator model, Bjorken estimate of the initial energy density, hadron structure and quark confinement,

hydrodynamics of Quark-Gluon Plasma and phase diagram, deconfinement phase transition, global

observables at RHIC and LHC energies, possible signatures of Quark-Gluon Plasma formation, dilepon

production, Drell-Yan Process in nucleus-nucleus collision, direct photon production, De-bye screening in

the QGP, J/ suppression in the QGP, strangeness enhancement, correlation and event-by-event

fluctuations, Handbury-Brown-Twiss effect, transverse mass, transverse energy, an isotropic flow and jet

quenching.

Unit-IV: Detectors in High Energy Physics Experiments

General characteristics of detectors:

Sensitivity, energy resolution and fano factor, detector efficiency and dead time.

Multiwire and Drift Chambers:

Ionization, drift and diffusion of charges in gases, pulse formation and its shape in proportional counters,

Multiwire proportional counter:-basic principle of working, construction and readout method, The drift

chamber:-principle of working, drift gases and spatial resoulution, Di-Muon Spectrometer of ALICE and

MuCh of CBM, Cerenkov counter and its applications.

Calorimetry in High-Energy Physics:

Idea of radiation length and critical energy, electromagnetic shower and hadronic shower detectors.

Review of some Major High Energy Physics Experiments:

Neutrino Flavour Oscillation experiments and Physics Scenarios at RHIC and LHC energies.

Books Recommended:

1. Pilkuhn, H. : The Interactions of Hadrons

2. Martin, L.P. : High Energy Hadron Physics (John Willey)

3. Collins, P.D.B. & Martin, A.D. : Hadron Interactions (Adam Hingler)

4. Hagedorn, R. : Relativistics Kinematics (Benjamin)

5. Perkins, D.H. : Introduction to High Energy Physics

(Addison Wesley)

6. Halzen, F. and Martin, A. : Quarks and Leptons (John-Wiley)

7. Wong, C.Y. : Introduction to High Energy Heavy Ion Collisions

(World Scientific)

8. Ferbel, T. : Experimental Techniques in High Energy Physics

(Addison Wesley)

9. Leo, W.R. : Techniques for Nuclear and Particle Physics Experiments (Narosa)

10. Kleinknecht, W. : Detectors for Particle Radiation (Cambridge)

(BOS: 30.5.2017)

Syllabus for M.Sc. III Semester

Nuclear Physics-A

Paper Code: PHM3022


Lectures: 40

Tutorials: 08

Unit-I: The Two-Nucleon Problem

The nucleon-nucleon potential:

Conservation laws and invariance principles, general form of the nucleon-nucleon potential., the tensor

potential, the V14 potential, nucleon-nucleon states.

The ground state of the deuteron:

Ground state of the deuteron and D-state admixture, Magnetic and electric quadrupole moments.

Electromagnetic properties of nuclei:

Transition probabilities, electric and magnetic multipole moments.

Unit-II: The Shell Model

General considerations, evidence of shell effects, average potential of the nucleus, spin-orbit coupling.

Symmetry properties, isotopic spin.

The extreme single particle model, the single particle model, seniority, reduced isotopic spin. Nordhe im’s

rule and ground state spins of odd-odd nuclei, configuration mixing. The independent particle model, LS

and JJ coupling schemes, experimental evidence of the single particle states.

Unit-III: The Deformed Shell Model and The Collective Model

The Deformed shell model:

Experimental evidence (Rotational bands, Very large quadrupole moments, Fission isomers, Single

particle structure, Strongly enhanced quadrupole transition probabilities, hexadecupole shapes, etc.),

General deformed potential, Nuclear rotational motion, rotational energy spectra and the nuclear wave

functions for even-even and odd-A nuclei, nuclear moments.

The Collective model (Bulk properties):

Deformation parameters, Nuclear shapes with quadrupole, octupole and hexadecupole deformations,

Collective oscillations and the liquid drop model, Kinetic energy and potential energy for quadrupole

deformations. The Nilsson model, coupling between modes of collective excitation: rotation-vibration

interaction, Rotation-particle coupling, core excitation.

Unit-IV: The Heavy-Ion Physics

Physical description of heavy ion interaction, elementary idea of classical and approximate quantum

mechanical theories, classical and semi-classical analysis of heavy ion reaction data, nuclear rainbow

scattering, exotic and super heavy nuclei, complete and incomplete fusion, idea of sub-barrier fusion,

high-spin states.

Books Recommended:

1. Deshalit, A. and Freshbach, H. : Theoretical Nuclear Physics, Vol.1: Nuclear Structure,

(JohnWiley)

2. Preston, M.A. and Bhaduri, R.K. : Structure of the Nucleus (Addison-Wesley).

3. Roy, R.R. and Nigam, B.P. : Nuclear Physics, Theory and Experiment (John-Wiley and Sons,

INC.)

4. Hodgson, P.E. et al. : Introductory Nuclear Physics (Oxford University Press).

5. Brinkk, D.M. : Semi-Classical Methods on Nucleus-Nucleus Scattering (Cambridge University

Press).

6. Allan Bromley, D. : Treatise on Heavy Ion Physics Vol. 3 & 4 (Plenum Press).

7. P Ring and P. Schuk (Springer) : The Nuclear many-body Problem.

8. P. E. Hodgson (Oxford) : The Heavy Ion Reactions.

9. Greiner (Springer) : The nuclear Models.

10. L. R. B. Elton : The Nucleus.

(BOS: 21.05.18)


String Theory

Paper Code : PHM-

M.M.: 100

Credits: 04

Lectures: 48

Tutorials: 08

Unit-I: Before String Theory

Achievements and problems with the standard model (SM) of particle interactions. Grand unified theories,

supersymmetry and supergravity. Spheres in various dimensions, Planck length in higher dimensions.

Unit-II: String Theory Primer

Point particle, relativistic strings, closed strings, world sheet and background aspects, bosonic string

theory, Gupta Bleuler, light cone and BRST quantizations, superstrings of type I, IIA, IIB and heterotic

strings.

Unit-III: Physical Aspects of String Theory

Compactification and supersymmetry breaking. Calabi-Yau manifolds and their mathematical properties,

examples of Calabi-Yau manifolds, T-Duality in presence of background fields, Low energy effective

actions, S-duality, M-Theory.

Unit-IV: AdS/CFT

Branes, D-brances & hints for gauge gravity duality in branes and scalar absorption. Maldacena

conjecture. AdS5 and AdS3 case. Applications.

Books Recommended:

1. Kiritsis, E. : String Theory in a Nut-shell (Princeton)

2. Becker, K., Becker,

M., Schwarz, J.H.

: String Theory and M-Theory (Cambridge)

3. Zwiebach, B. : A First Course in String Theory (Cambridge)

OLD


String Theory



Lectures: 48

Tutorials: 08

Unit-I: Before String Theory

Review of achievements of standard model of particle physics as well as standard cosmological model.

Very brief but technical overview of problems with the standard model (SM) of particle interactions,

grand unified theories, supersymmetry and supergravity. Spheres in various dimensions, Planck length

in higher dimensions.

Unit-II: String Theory Primer

Point particle, relativistic strings, closed strings, world sheet and background aspects, bosonic string

theory, Gupta Bleuler, light cone and BRST quantizations, superstrings of type I, IIA, IIB and

heterotic strings.

Unit-III: Mathematical Panorama

Computification and supersymmetry breaking.

Calabi-Yau manifolds and their mathematical properties, examples of Calabi-Yau manifolds,

The bosonic string and Dp-Branes, D-branes in type-II superstring theories, T-Duality in presence of

background fields, Low energy effective actions, S-duality, M-Theory, F-Theory.

Unit-IV: Exotic Reality

String theory and matrix models.

Applications of string theory techniques in other branches of Physics.

Black Holes in general relativity, black hole thermodynamics, blackholes in string theory.

Gauge/String Duality, AdS/CFT correspondence.

Books Recommended:

1. Kaku, M. : Quantum Field Theory (Oxford)

2. Kiritsis, E. : String Theory in a Nut-shell (Princeton)

3. Becker, K., Becker,

M., Schwarz, J.H.

: String Theory and M-Theory (Cambridge)

4. Zwiebach, B. : A First Course in String Theory (Cambridge)

(BOS: 30.5.2017)


Physics of Nano Materials

Paper Code: PHM3023 M.M. : 100 Credits: 04

Lectures: 48

Tutorials: 08

Unit-I: Introduction to Nanomaterials and Properties

Brief history and overview of nanomaterials; Synthesis techniques: Top down and Bottom up

approaches (High energy ball milling, Sol-gel process, Chemical bath deposition, Plasma Arc discharge,

Chemical vapor deposition, Sputtering, Pulsed Laser deposition, Molecular beam epitaxy).

Mechanical, Thermal, Electrical, Magnetic and Optical properties.

Unit-II: Characterization tools of Nanomaterials Scanning Probe Microscopy (SPM): Scanning Tunneling Microscopy (STM), Local density of states,

Tunneling current, Applications, Atomic Force Microscopy (AFM); Electron Microscopy: Scanning

Electron Microscope (SEM), Transmission Electron Microscope (TEM), High resolution TEM.

Unit-III: Carbon based Nanomaterials Nature of carbon bond, Carbon structures, Small carbon clusters; Fullerenes: Synthesis and

Properties, various forms of fullerene materials; Graphene: Synthesis and Applications; Carbon

nanotubes: classification, synthesis, properties (Electrical, Vibrational & Mechanical) and applications,

Nanodimond.

Unit-IV: Quantum Nanostructures and Nanostructured Ferromagnetism Quantum wells, wires and dots, Fabrication of Quantum Nanostructures, Size effect, Conduction

electron and dimensionality, Fermi gas and density of states. Partial confinement, Single electron

transistor (SET), Single electron capacitor, Quantum effects on SET, Fabrication of SET, Bulk

Nanostructuring and Magnetic properties, Dynamics of Nanomagnets, Nanopore containment of

magnetic particles.

Books Recommended:

1. Poole Jr., C.P. & Owens, F.J.

: Introduction to Nanotechnology (Wiley Interscience)

2. Edelstein A.S., and Cammarata, R.C.

: Nanomaterials: Synthesis, Properties and Applications Edn. (Institute of

Physics)

3. Fujita, F.E. : Physics of New Materials, Second Edn. (Springer-Verlag)

4. Zhen Guo, Li Tan : Fundamentals and Applications of nanomaterials

5. Gaber L. H. Harry F.

Tibbals, Joydeep Dutta

and John J. Moore

: Introduction to Nanoscience and Nanotechnology (CRC Press).

6. K.K. Chattopadhyay & A.N. Banerjee

: Introduction to Nanoscience & Nanotechnology (PHI Learning Pvt. Ltd.)

7. Michael F. Ashby, Paulo

J. Ferreira & Daniel L.

Schodek

: Nanomaterials, Nanotechnologies and Design (Elsevier)

Syllabus for M.Sc. (Physics) Semester-III Programming and Computational Physics-A

Paper Code : PHM3031 M.M.: 50 Credits: 02

Lectures: 20

Tutorials: 04

Unit I

Basic concepts of Object Oriented Programming (OOP); benefits and application of OOP; Introduction to

C++ language and its application; C/C++ statements, Structure of C++ program, creating source file,

compiling and linking. Identifiers and Keywords.

Constants: String, Numeric, Character constants; Variables: integer, float and character variables, local

and global variables

Operators: Arithmetic, logical operators

Type conversion; declaration of constants and variables

Exercises

Unit II

Input / output: scanf(), printf(), cin, cout statements, Unformatted/ Formatted I/O operations

Control and iterative statements: simple if, if-else, nested if, switch-case statements, while and do-while

loop, for loop, Break, continue statements, goto statement and the conditional expression (? : operator);

Simple programs based on these statements

Unit III

Header files: standard and user defined

Functions: Introduction, types of functions, in-built functions, defining functions, arguments, function

prototype, parameters, calling functions, return statement, recursion. Void function and function returning

results

File handling: file concepts, file creation, I/O operations on files and file functions, stream state member function. Opening, closing and rewinding a file, reading data from a file, writing output to a file.

Unit IV

Arrays: notations, declaration and initialization, multidimensional arrays

Pointers: definition, applications of pointers, pointer declaration, pointer operator, address operator,

pointer expressions, pointer arithmetic. Pointers and function call by value and by reference. Pointers to

functions. Pointers and arrays. Dynamic, memory allocation.

Structure: declaration and initialization. Functions and structures.

Unions: The union tag, processing with unions, Initialization of unions.

Exercises

References:

1. Object-oriented Programming with C++, E. Balagurusamy

2. Programming with C++, John Hubbard and Atul Kahate

3. Practical C++ Programming, Stew Oualline

4. Thinking in C Including Object Oriented Programming with C++, P.B. Mahapatra


Instrumentation and Analytical Methods-A



Lectures: 24

Tutorials: 04

UNIT-I: Transducers

Transducers:Temperature, magnetic field and vibration, linear position transducer:

Piezoelectric. Optical detectors.

UNIT-II: Signal Measurement

Signal conditioning and recovery, impedance matching, amplification (Op-amp based, instrumentation

amp, feedback), filtering and noise reduction, shielding and grounding; lock-in detector, box-car

integrator, modulation techniques.

UNIT-III: Spectroscopy Techniques-I

Fourier transforms infrared spectroscopy (FTIR). FTIR Microscopy and ATR-FTIR. Raman spectroscopy

: Dispersive, FT- Raman and micro Raman spectroscopy. Raman Imaging.

UNIT-IV: Spectroscopy Techniques-II

UV-Visible spectroscopy. Fluoresence and Photoluminiscence Spectroscopy. X-ray Fluorescence and

Atomic Absorption Spectrometry.

Reference Books:

1. Spectroscopy Volume 1, 2 and 3: B.P. Straughan and S. Walker.

3. Long, D.A. : Raman Spectroscopy (McGraw Hill, New York)

4. Herzberg, G. : Molecular Spectra & Molecular Structure Vol. II & III (D. Van

Nostrand)

5. Griffiths, P.A. : Fourier Transform Infrared Spectroscopy (John Wiley & Son).

6. Lakowicz,J.R. : Principles of Fluorescence Spectroscopy

7. Demtroder, W : Laser Spectroscopy (Springer Verlag)

1. A.K. Ghosh : Introduction to Measurements and Instrumentation, , 3rd Edition, PHI, Learning Pvt. Ltd.

2. D.V.S. Murty : Transducers and Instrumentation, , 2nd Edition, PHI Learning Pvt. Ltd.

3. C.S. Rangan, G.R.

Sarma, V.S.V.

Mani

: Instrumentation Devices and Systems, Tata McGraw Hill

4. D. Patranabis : Principles of Electronic Instrumentation, , PHI Learning Pvt. Ltd.


Atmospheric Physics


M.M.:50 Credits: 02

Lectures : 24

Tutorials: 04

Unit – I: Elements of Atmosphere and Physical Meteorology

Atmospheric composition, laws of thermodynamics of the atmosphere, Adiabatic processes, potential

temperature, The Clausius-Claperon equation, radiative transfer and the laws of black body radiation,

solar and terrestrial radiation.

Unit – II: Dynamical Meteorology

The fundamental forces, hydrostatic equation, Lapse rate, Enthalpy equation, Entropy of dry air and

entropy change, The circulation theorem, vorticity, potential vorticity and potential vorticity equations.

Unit – III: Numerical Methods in Atmospheric Physics

The finite difference method, the finite difference equation for sound, gravity and Rossby waves, filtering

of gravity and Rossby waves, The equivalent-Barotropic model, essentials of numerical weather analysis

and forecasting.

Unit – IV: Observational Techniques in Atmospheric Physics

Conventional observational techniques, conventional measurement of pressure, temperature, humidity,

wind, precipitation, visibility.

Modern Observational Techniques: LIDARS, SODARS, RADARS.

Text and Reference Books:

1. Salby, M.L. : Fundamentals of Atmospheric Physics (Academic Press)

2. Vallace, J.M.

and

Hobbs, P.W.

: Atmospheric Science: An Introductory Survey (Academic Press)

3. Holton, H.R. : An Introduction to Dynamic Meteorology (Academic Press)

4. Iribarne, J.V.

and Godson,

W.L.

: Atmospheric Thermodynamics (D. Reidel)

5. Thomson,

P.D.

: Numerical Weather Analysis and Prediction (Macmillan)

6. WMO Guide to Meteorological Instrument and observing Practices WMO – Report No.8, TP 3,

Secretariat of the WMO, Geneva-Switzerland.

Syllabus for M.Sc. (Physics) Semester III

Elective Paper: Quantum Field Theory

Paper Code: PHM3034

MM: 100

Credit: 04

Lectures: 48

Tutorials: 08

Unit I: Path integral in quantum mechanics (10 Lectures)

Path integral formulation of quantum mechanics, harmonic oscillator problem in path integral formalism,

revision of canonical quantization for scalar, Dirac and gauge fields, functional integrations and

differentiations, Grassmann variables, functional integrations and derivatives over Grassmann variables.

Unit II: Path integral quantization (10 Lectures)

Path integral for scalar fields, generating functional, 2-point function, n-point functions and Wicks

contraction, interacting theory, Feynman diagrams in configuration space, connected diagrams, Feynman

diagram in momentum space, Greens functions, 1-loop diagrams, path integral for Dirac field.

Unit III: Path integral quantization of electromagnetic field (10 Lectures)

Path integral for electromagnetic field, gauge fixing, Faddeev-Popov procedure, symmetries and Ward

identities, LSZ reduction for the gauge field and scattering amplitudes.

Unit IV: Renormalization in QED (10 Lectures)

Renormalization of photon propagator, electron propagator and QED vertex function, QED beta function

at one loop, renormalization group evolution and running coupling.

References

1. F. Mandl and G. Shaw, Quantum Field Theory, 2nd edition, Wiley publication.

2. L. H. Ryder, Quantum Field Theory, 2nd edition, Cambridge University Press.

3. Mark Srednicki, Quantum Field Theory, 1st edition, Cambridge University Press.

M.Sc. (Physics) III Semester

List of Experiments

PHM- C Lab

1. To determine the recovery time of a G.M. counter using two source method.

2. To plot -ray spectra of three gamma sources using Nal(TI) scintillation spectrometer and to draw calibration and resolution curves.

3. To produce and measure low and high vacuum in the given vessel.

4. To study 16, 4-bit word RAM (7489) and to perform reading and writing exercises.

5. To determine the ‘g’ factor of electron by electron spin resonance method.

6. To sketch some interaction events (stars) produced in nuclear emulsion and to measure

projected angles of at least five tracks.

7. To use the operation amplifier for solving the given simultaneous equations.

8. (i) To study the double slit diffraction pattern using a solid state LASER and to determine the

separation between slits.

(ii) To study the Airy’s disc pattern and to determine the diameter of a circular aperture.

9. Rutherford scattering of alpha particle.

List of experiments


PHM-DSE Lab. A: Condensed Matter Physics

1.

Calculate the ultrasonic velocity ii water and hexane using ultrasonic interferometer.

2. Study the dispersion relation of monatomic and diatomic lattices using lattice dynamics kit.

3. Estimate the band gap energy of a semiconductor by measuring reverse saturation current at

different temperatures.

4. Determine the resistivity of a given semiconductor by four probe method at different

temperatures and hence calculate the energy gap.

5. Plot the dielectric constant as a function of temperature for a given ferroelectric material and hence find the Curie temperature.

6. (i) Determine the reverse saturation current and material constant () of a given semiconductor material.

(ii) Find out the temperature coefficient of junction voltage for a p-n junction diode.

(iii)

Study of variation of depletion capacitance with reverse bias voltage of p-n junction diode.

7. Record the x-ray diffraction patter of a given sample using different x-ray sources (Cu, Fe, Mo)

and hence find the energies of these sources.

List of experiments


PHM-DSE Lab A :Nuclear physics

1. To study the X-ray fluorescence and to verify the Moseley’s law.

2. To study the Compton scattering of -rays and to determine the rest

mass of electron.

3. To obtain the -ray spectra of 90Sr and 22Na and to find out the most

frequent decay energies of these sources.

4. To determine the window thickness of -counter using two -

sources (90Sr, 204Tl).

5. To study the resolution of NaI(Tl) detector with biasing voltage and to

find the optimum operating voltage.

List of experiments


PHM-DSE Lab A: Electronics

1. To measure the centre (free-running) frequency of a phase-locked loop (IC 565). To observe the

lock range and measure the maximum and minimum capture frequencies for different centre

frequencies.

2. To study the SMPS (IC 34063) as a

(i) Step-up

(ii) Step-down and

(iii) Inverting switching regulators.

3. To study the IC XR-2206 as a function generator and frequency-shift keying (FSK) action.

4. To design a fixed voltage D.C. power supply using Zener diode and to study its ripple factor

using Pspice software.

List of Experiments


PHM-DSELab. A: Atomic, Molecular and Optical Physics

1. Measurement of Band positions and determination of vibrational constants of N2 molecule.

2. Measurement of Band positions and determination of vibrational constants of AlO molecule.

3. Recording of Iodine absorption spectrum and determination of vibrational constants.

4. Study of Image forming properties of laser with the help of low L.P.I. grating and determination of

laser wavelength.

5. Determination of Bohr Magnetron using Zeeman effect.

6. Determination of characteristic parameters of optical fibre and study of optical communication.

7. Recording and identification of rotational spectrum of CN.

Syllabus for M.Sc. (Physics) Semester-IV

Molecular Physics

Paper Code: PHM-4012


Lectures: 48

Tutorials: 08

Unit-I: Molecular Symmetry and Vibrations Spectra

Elements of symmetry. Point groups. Matrix representation of symmetry elements of a point group.

Reducible and irreducible representations. Point group character tables: C2v and C3v . Normal modes.

Distribution of normal modes in symmetry species. Vibrational selection rules. Group vibrations.

Aharmomonicity: anharmonic vibrations, Fermi and Darling-Dennison resonance. Inversion vibration.

Unit-II: Rotational and Vibration-rotation Spectra of Polyatomic

Molecules Rotational spectra of linear molecules. Intensities. Vibrational satellites. Coriolis interaction and effect of

l-type doubling in linear molecules. Rotational spectra of symmetric (prolate and oblate) and

asymmetric rotor molecules. Nuclear spin statistical weights and their effect on intensities. Structure

determination from rotational constants.

Vibration-rotation spectra of polyatomic molecules: Parallel and perpendicular bands of linear molecules

and symmetric top ( prolate and oblate) molecules.

Unit-III: Molecular Orbital Theory and Electronic Spectra

Molecular Orbitals. LCAO treatment of H2+ and H2, Heitler and London theory for H2. Rydberg orbitals.

Crystal field and Ligand field molecular orbitals.

Fluorescence Spectroscopy, Quantum yield, Kasha’s Rule, Jablanski diagram , Time- resolved

Fluorescence, Determination of excited state life time.

Unit-IV: Experimental Techniques in Spectroscopy

Microwave spectroscopy, Fourier transform spectroscopy, Matrix isolation spectroscopy.Linear Raman

spectroscopy, Non-linear Raman spectroscopy: Stimulated Raman spectroscopy, coherent anti-stokes Raman

scattering, resonance Raman spectroscopy, hyper Raman effect. Surface -Enhanced Raman Scattering.

Books Recommended:

1. Barow, G.M. : Introduction to Molecular Spectroscopy (McGraw Hill)

2. Hollas, J.M. : High Resolution Spectroscopy (John Wiley)

3. Townes, C. : Microwave Spectroscopy (Dover)

4. Long, D.A. : Raman Spectroscopy (McGraw Hill, New York)

5. Herzberg, G. : Molecular Spectra & Molecular Structure Vol. II & III (D. Van

Nostrand)

7. Griffiths, P.A. : Fourier Transform Infrared Spectroscopy (John Wiley & Son).

8. Lakowicz,J.R. : Principles of Fluorescence Spectroscopy 9. Demtroder, W : Laser Spectroscopy

(Springer Verlag)


Condensed Matter Physics- B



Lectures: 48

Tutorials: 08

UNIT-I

Magnetism: Weiss theory of ferromagnets and Curie-Weiss law, Neel model of antiferromagnetism and ferrimagnetism. Spin waves, magnons in ferromagnets, dispersion relation (classical treatment), Bloch T

3/2

law; magnons in antiferromagnets, dispersion relation (classical treatment). Nuclear paramagnetism.

Cooling by adiabatic demagnetization.

Magnetic Resonance: Electron spin resonance (ESR). Nuclear magnetic resonance (NMR). Spin

relaxation (spin-lattice, spin-spin). Applications.

UNIT-II

Defects: Diffusion. Colour centres: production and properties. Excitons (Frenkel, Mott-Wannier),

dispersion, experimental studies (alkali halide and molecular crystals). Polarons.

Pyroelectricity and Ferroelectricity: Pyroelectric and ferroelectric crystals. Polarization catastrophe, soft

modes. First and second-order phase transitions, Landau theory of phase transition, experiments on

ferroelectric crystals. Antiferroelectricity. Piezoelectric crystals, applications.

UNIT-III

Surfaces and Interfaces: Reconstruction and Relaxation, Surface Crystallography, Reflection high energy

electron diffraction (RHEED), Surface electronic structure, Work function, Thermionic emission, Surface

states, tangential surface transport, Magnetoresistance in two dimensional channel, Integral Quantized

Hall Effect (IQHE), Fractional Quantum Hall Effect, Solar Cell’s and Photovoltaic detectors, Alloys:

Substitutional Solid Solution, Hume-Rothery Rules Order-disorder transformation, Elementary Theory of

orders, Kondo effect.

UNIT-IV

Superconductivity: Distinction between an ideal conductor and a super-conductor. Thermodynamic

properties. Heat capacity and energy gap. Isotope effect and BCS theory, important predictions of BCS

theory. Ginzburg-Landau theory, London equation., flux quantization, coherence length, Giaever

tunneling, Josephson tunneling, supercurrent quantum interference.

High temperature superconductors, salient features. Qualitative discussion on applications of

superconductors.

Books Recommended:

1. C. Kittel : Introduction to Solid State Physics 8th

Ed. (John-Wiley)

2. Srivastava, J.P. : Elements of Solid State Physics (Prentice-Hall)

3. Ashcroft, N.W. and

Mermin, N.D.

: Solid State Physics, (Saunders College)

4. Ziman, J.M. : Principles of the Theory of Solids (Vikas)


High Energy Physics B



Lectures: 48

Tutorials: 08

Unit-I: Discrete Symmetries and Weak Interactions

Elementary particles and their interactions, Quark and leptons. Discrete symmetries, C, P, T symmetries

and CPT theorem (without proof) and its consequences. Parity of leptons and anti-leptons, Parity of quarks

and hadrons, Parity of charged and neutral pions, Parity of Photon, C-Parity of neutral pion and eta.

Parity violation in -decay, Measurement of Helicity of Neutrino, Bilinear covariants, V-A theory of weak

interactions and current Lagrangian. Properties of weak currents, Neutrino-electron scattering, CVC and

PCAC. decay.

Unit-II: Nucleon Structure and Quark Model

Nucleon as a composite particle. Nucleon resonances and baryon spectroscopy. Isospin: SU(2), SU(3)

symmetry and classification of particles and resonances. Quark model of hadrons, spin and flavour SU(6)

wave functions of mesons and baryons. Mass formula for baryons and mesons. Calculation of magnetic

moments.

Unit-III: High Energy Lepton-Nucleon Scattering

e--

- scattering.

Elastic-electron-nucleon scattering: Matrix element, Rosenbluth cross section formula, nucleon form

factors and their q-dependence. Electric and Magnetic Sachs form factors, Comparison with experimental

results.

Deep inelastic electron-nucleon scattering: Kinematics and cross section formula. Experimental results.

Bjorken scaling. Nucleon structure functions and partons. Electron-quark scattering.

Unit-IV: Physics of heavy flavor particles

Phenomenology of strange particles and their semileptonic and nonleptonic decays. Cabibbo theory.

Neutral kaon decays and CP violation. Flavor oscillation, Discovery of quarks, Charm, bottom and top

quarks. Quarkonium and their spectra. Predicted c-cbar and b-bbar states with principal quantum numbers

n= 1 & 2 with their properties. The quark-antiquark potential, Lepton-Quark symmetry, Quark mixing,

CKM matrix (idea).

Books Recommended:

1. Halzen, F and Martin, A.D. : Quarks and Leptons (John-Wiley)

2. Close, F.E. : Quarks and Partons (Academic Press)

3. Martin, B R and Shaw, G

Particle Physics (John-Wiley)

(BOS: 30.5.2017)

Syllabus of M.Sc. (Physics) Semester-IV

Nuclear Physics (B)



Lectures: 40

Tutorials: 08

Unit-I: Nuclear Reactions

Types of nuclear reactions.

The Collision matrix:

The s-wave scattering, Collision matrix, Unitary and symmetry properties of the collision matrix. The

Reciprocity. Definition of the R-matrix. The resonance scattering, Briet-Wigner one level formula.

The Optical model:

The nuclear optical potential, Optical model at low energies, formal derivation of the optical model

potential.

Unit-II: The Direct Reactions

Compound nucleus theory and its limitations, Ghoshal’s experiments, Kinematics and theory of stripping

and pick-up reactions, Statistical theory of reactions.

The high energy approximation and the Glauber theory: The Eikonal approximation, the high energy potential scattering, Glauber model for nucleon-nucleus and

nucleus-nucleus scattering.

Unit-III: Many-Body Theories

Non relativistic theories:

Nuclear matter, the Goldstone expansion, reaction matrix, Bruckner-Bethe-Goldstone integral equation,

coordinate space correlation wave function, properties of reaction matrix.

Relativistic Mean Field Theory (RMF):

Mean Field Theory, Lagrangian density, Dirac equation and Field expansion, Hamiltonian density, nuclear

matter, Neutron Matter (Equation of state).

Unit-IV: Electromagnetic and Weak Interactions in Nuclei

The Electromagnetic Interaction:

Electromagnetic current and its interaction with nucleons and nuclei. Electron scattering from nucleons

and nuclei. Four-momentum transfer and the Mott scattering, the nucleon and nuclear form factors and

their experimental determination, Electric and Magnetic Sachs form factors.

The Weak Interaction:

The -decay and weak currents, Fermi theory., The V-A theory of weak interactions, inelastic

nutrinoproton scattering. The weak form factors, Deep inelastic scattering, Scale invariance and Partons.

Books Recommended:

1. Wong, S.M. : Introductory Nuclear Physics, (Prentice Hall)

2. Preston, M.A. : Physics of the Nucleus, (John Wiley)

3. Preston, M.A. & Bhaduri, R.K. : Structure of the Nucleus, (Addison Wesley)

4. Roy, R.R. & Nigam, B.P. : Nuclear Physics, Theory and Experiment, (John Wiley)

5. de Shalit, A & Feshbach, H. : Theoretical Nuclear Physics, Vol.I, Nuclear Structure, (John Wiley).

6. Rev. of Modern Physics, Vol. 39 (1967) p. 719.

7. Ed. Y. K. Ghambir : Mean Field Theory of Nuclei.

8. J. D. Walecka (Oxford Press) : Theoretical nuclear and subnuclear Physics.

9. D. H. Perkins (Edison Wesley) : Introduction to High Energy Physics.

10. R. J. Glauber : Lectures in Theoretical Physics, Vol. 1, edited by: W. E Brittin and L.

G. Dunham, (Interscience Publishers, Inc. New York, 1959).


Physics of Lasers and Laser Applications


M.M.: 100

Credits: 04

Lectures: 40

Tutorials: 08

Unit-I: Laser Characteristics

Gaussian beam and its properties. Optical Resonators: Various types of resonators, spatial field

distributions in open resonators, confocal resonators, frequency spectrum of a confocal resonator, Stability

of resonators:‘g’ parameter, Q switching. Mode locking: Active and passive mode locking. Generation of

femtosecond pulses.

Unit-II: Laser Systems

Principle and working of different Lasers: Argon ion laser. Neodynium-YAG laser. Neodymium glass

laser. Dye Lasers. Tunable solid state lasers: Color center lasers. Titanium sapphire laser. Free electron

lasers. Chemical lasers. Semiconductor diode lasers.

Unit-III: Nonlinear Optical Mixing Technique

Nonlinear susceptibility, second harmonic generation, phase matching, optical mixing, sum frequency and

higher harmonic generation, difference-frequency spectrometer. Optical parametric oscillators. Self-

focusing of light. Tunable Raman lasers.

Unit-IV: Applications of Lasers

Principle of LIDAR, atmospheric measurements with LIDAR. Laser-induced- breakdown spectroscopy

and its applications. Optical fibres and optical communication. Holography and its applications. Laser

cooling and trapping of atoms: Magneto-Optical Trap, Evaporative cooling, Bose-Einstein condensation.

Books Recommended:

1. Demtroder, W. : Laser Spectroscopy (SpringerVerlag)

2. Svelto, O. : Principle of Lasers (Plenum Press)

3. Laud, B.B. : Lasers and Nonlinear Optics (Willey Eastern)

4. LASERS:Theory&Application : Thyagarayan,K. and Ghatak, A.K.

OLD


Standard Model of Particle Interactions



Lectures: 40

Tutorials: 08

Unit I: Symmetries and Quantum Electrodynamics

Action principle, relativistic field, invariance and conservation, Lie groups and internal symmetries, the

Poincare group and its generators. QED: Global and local gauge invariances in quantum mechanics and

field theory, gauge field, covariant derivative, QED as a gauge theory.

Unit II: Yang-Mills Theories

Explicit construction of non-abelian (Yang-Mills) gauge theory and its consequences. Need for colour,

QCD Lagrangian, running coupling, confinement and asymptotic freedom. Hidden symmetry,

spontaneously broken discrete and continuous symmetries, Goldstone theorem, Goldstone model, Higgs

Mechanism.

Unit III: Salam-Weinberg Model

Week isospin and hypercharge, Glashow-Salam-Weinberg model for leptons, gauge group, various pieces

of the Lagrangian, mass generation of gauge bosons and fermions, neutrino electro scattering extension to

hadrons and GIM mechanism and CKM matrix.

Unit IV: Applications and Beyond the Standard Model

Applications in leptonic sector, Z, W and Higgs, and other processes.

Beyond standard model: GUTS, SUSY, SUGRA and String Theory.

Books Recommended:

1. Sterman, G. : Quantum Field Theory (Cambridge)

2. Quigg, C. : Gauge Theoreis of the Strong, Weak and Electromagnetic

Interactions (Benjamin-Cummings)

3. Burgess, C. and

Moore, G.

: The Standard Model (A Primer) (Cambridge)

4. Cottingham, W.N. and

Greenwood, D.A.

: An Introduction to the Standard Model of Particle Physics

(Cambridge)

(BOS: 21.05.18)


Standard Model of Particle Interactions

Paper Code: PHM-

M.M.: 100

Credits: 04

Lectures: 48

Tutorials: 08

Unit I: Symmetries and Quantum Electrodynamics

Lagrangian dynamics, symmetries and conservation laws. QED: Global and local gauge invariances in

quantum mechanics and field theory, minimal e.m. substitution, gauge field, covariant derivative, QED as

a gauge theory, Applications of QED.

Unit II: Yang-Mills Theories

Explicit construction of non-abelian (Yang-Mills) gauge theory and its consequences. Need for colour,

QCD Lagrangian, running coupling, confinement and asymptotic freedom. Applications of QCD to DIS,

Collider Physics.

Unit III: Salam-Weinberg Model

Hidden symmetry, spontaneously broken discrete and continuous symmetries, Goldstone theorem,

Goldstone model, Higgs Mechanism, Glashow-Salam-Weinberg model for leptons, various pieces of the

Lagrangian, mass generation of gauge bosons and fermions, extension to hadrons and GIM mechanism.

Unit IV: Renormalization and Anomalies

Renormalization of QED, Faddeev-Popov ghosts, regularization schemes, renormalization of

spontaneously broken gauge theories, Wilson’s approach, anomalies, grand unified theories and beyond.

Books Recommended:

1. Sterman, G. : Quantum Field Theory (Cambridge)

2. Quigg, C. : Gauge Theoreis of the Strong, Weak and Electromagnetic

Interactions (Benjamin-Cummings)

3. Burgess, C. and

Moore, G.

: The Standard Model (A Primer) (Cambridge)

Syllabus for M.Sc. (Physics) Semester IV

Quantum Optics



Lectures: 48

Tutorials: 08

Unit I: Non-linear optics and quantization of radiation field

Coherence. Nonlinear optics. Second-order nonlinear phenomena, Phase-matching, Field quantization,

Light as a quantum harmonic oscillator, coherent state and squeezed light, photon number states.

Unit II: Photon statistics

Photon counting statistics, Classification of light by photon statistics, Semi-classical and quantum theory

of photodetection, Photon antibunching. Hanbury Brown-Twiss experiments, Second order correlation

function

)(2 g .

Unit III: Light-matter interaction

Resonant light matter interactions, Two-level atom approximation, Density matrix formulation. Optical

cavities. Atom-cavity coupling, Weak coupling regime - Spontaneous emission and Purcell effect

(spontaneous emission in a single mode cavity), Strong coupling regime - Cavity quantum

electrodynamics.

Unit IV: Quantum information processing

Basic principles of quantum cryptography, Quantum key distribution with BB84 protocol and single

photon sources, Quantum bits (qubits). Quantum logic gates and applications of quantum computers.

Entangled states, Single photon interference, Bell's theorem and Quantum teleportation.

Reference books

1. Mark Fox. Quantum Optics: An Introduction. Oxford University Press (Oxford Master Series

in Physics), (2007).

2. Rodney Loudon. The Quantum Theory of Light. Clarendon Press - Oxford, 3rd Ed. (2000). 3. Marlan O. Scully and M. Suhail Zubairy, Quantum Optics. Cambridge University Press-

Cambridge (1997)

(BOS: 30.5.2017)

Syllabus of M.Sc. IV Semester

Quantum Electrodynamics


Credit: 04

Lectures:40

Tutorials:08

Unit I : Quantization of electromagnetic field

Brief review of classical theory and canonical quantization of the electromagneic field, gauge invariance,

problem with quantization, gauge fixing, QED propagator, quantization in Coulomb gauge and Lorentz

gauge, symmetry properties, unitarity and expansion of S-matrix.

Unit II : QED at tree level

Feynman rules for QED, Lagrangian for a basic vertex, lowest order processes of QED, electronelectron

scattering, Bhabha scattering, photon bremsstrahlung. (Tutorial problems based on trace algebra, spin and

polarization sums, invariant matrix elements and cross-section formula for all three processes).

Unit III : QED at one loop

Ultraviolate and infrared divergences, dimensional regularization technique, electron self energy - mass

renormalization, vacuum polarization - field renormalization, vertex function - charge renormalization.

Unit IV : Applications of QED

Anomalous magnetic moment of the electron, correction to Lande g-factor, modification to Coulomb

interaction, Lamb shift, running of QED coupling, Landau pole.

References:

1. F. Mandl and G. Shaw, Quantum Field Theory, 2nd edition, Wiley publication.

2. L. H. Ryder, Quantum Field Theory, 2nd edition, Cambridge University Press.

3. Amitabha Lahiri and Palash. B. Pal, A first book of Quantum Field Theory, Narosa Publishing

House.

4. W. Greiner and Reinhardt, Quantum Electrodynamics, Springer-2009.

Syllabus for M.Sc. (Physics) Semester-IV Programming and Computational Physics-B



Lectures: 20

Tutorials: 04

Unit I

Review C++ and Object Oriented Programming,

Classes and Objects: classes, class definition, Declaration of class, member functions, defining the object

of a class, accessing a member of class, base classes and derived classes

Constructors and destructors: copy constructor, default constructor

Debugging a C++ program

Exercises

Unit II

Problem Solving: Evaluation of mean, variance, standard deviation; straight line fitting.

Monte Carlo Method: natural and pseudo random numbers, generation of random numbers: Mid square

and multiplicative congruential methods. Quality test of random numbers: uniform distribution and

autocorrelation tests, Gaussian and exponential distribution.

Unit III

Determination of pi, Simulation of random physics phenomena, Brownian Motion, Radioactive decay law

Evaluation of functions using power series: sin, cos, log, exponential functions etc.

Numerical Integration: Trapezoidal and Simpson rules

Differential equations: Solving second order differential equations using fourth order Runge-Kutta

Method.

Unit IV

Matrix operation, solving linear equations system, root finding: quadratic equation etc.

Odd calculations in sports, constructing prime number generator, dice construction.

Interfacing a C++ program with program in other computational languages e.g. FORTRAN, Python.

References:

1. Programming with C++, John Hubbard and Atul Kahate

2. Practical C++ Programming, Stew Oualline

3. A First Course in Computational Physics, Paul Devries, Javier E. Hasbun

4. Computer Simulation in Physics, R.C. Verma

5. Numerical Recipes in C++, William H. Press, Saul A Teukolsky, William T Vetterling, Brian P

Flannery

(BOS: 30.5.2017)


Instrumentation and Analytical Methods-B


M.M.:100 Credits : 02

Lectures: 24

Tutorials: 04

Unit-I

X-ray diffraction (XRD): Powder diffraction, Phase identification, Grain size and strain

determination, Small angle x-ray scattering and its applications, Low temperature generation and

measurement.

Unit-II Two and four probe resistivity measurement methods; Dielectric properties and measuring

technique; X-ray photo electron spectroscopy (XPS) and Auger Electron Spectroscopy (AES):

Instrumentation and applications.

Unit-III Scanning Tunneling Microscope (STM), Atomic Force Microscopy (AFM): Different operational

mode and typical applications.

Electron Microscopy: Field Emission Scanning Electron Microscope (FE-SEM), Field Emission

Transmission Electron Microscope (FE-TEM), Energy dispersive x-ray spectroscopy (EDS)

Unit-IV Thermal analysis techniques: DTA, DSC, TGA and STA; Magnetic measurement systems:

Vibrating Sample Magnetometer (VSM), Superconducting Quantum Interference Device (SQUID),

Electron Spin Resonance (ESR).

Books recommended: 1. D.J. O’Conor, B.A. Sextton,

R. St.C. Smart

: Surface Analysis Methods in Material Science

(Springer 2003) 2. A.D. Helfrick & W.D.

Cooper

: Modern Electronic Instrumentation and Measurement

Techniques (PHI 1996)

3. J.P. Bentley : Principles of Measurement Systems

(Pearson Education Ltd. England 2005).

4. A. Ghatak & K.K.

Thyagrajan

: Optical Electronics (C.U.P. 1993)

5. Y. Leng : Materials Characterization: Introduction to Microscopic &

Spectroscopic Methods, I-Edn. (John Wiley & Sons, 2008)

6. S. Zhang Liu Li &

Ashok Kumar

: Materials Characterization Techniques (CRC Press 2009)

7. G.S. Upadhyay & Anish

Upadhyay

Material Science & Engineering (Viva Books 2010)

8. Dieter K. Schroder : Semiconductor Material & Device Characteirzation

(Wiley IEEE Press 2006)

9. Rohit P. Prasan Kumar &

Antoinette J. Taylor : Optical Techniques for Solid State Materials Characterization

(CRC Press 2011).

Syllabus for M. Sc. (Physics) Semester-IV

Environmental Physics


Credit: 02

Lectures: 24

Tutorials: 04

Unit I: Essentials of Environmental Physics

Structure of the atmosphere; Temperature variations with height. Radiation temperature of the earth and

Greenhouse effect. Transport of matter, energy and momentum in nature; Raynold’s transport theorem,

energy and momentum equations. Hydrostatic equilibrium. Stratification and stability of atmosphere.

Unit II: Solar and Terrestrial Radiation

Physics of radiation. Interaction of light with matter, Lambert’s law. Rayleigh and Mie scattering. Laws of

radiation and their implication for radiative processes on earth and its environment. Solar and terrestrial

spectra. UV radiation. Ozone depletion problem. Energy balance of the earth atmosphere system.

Unit III : Environmental Pollution and Renewable Sources of Energy

Elementary fluid dynamics. Diffusion. Air, water and noise pollution. Air and water quality standards.

Heat island effect. Land and see breeze. Gaseous and particulate matters. Renewable sources of energy.

Solar energy, wind energy, hydropower, fuel cells and nuclear energy.

Unit IV : Global and Regional Climate

Elements of weather and climate modeling. Basic equation and dynamics of atmosphere. General

circulation of atmosphere and oceans. Global warming and climate change. Enhanced Greenhouse effect.

Books Recommended:

1. Boeker, E & Groundelle, R.V. : Environmental Physics (John Wiley)

2. Houghton, J.T. : The Physics of Atmosphere (Cambridge Univ. Press, 1977)

3. Houghton, J.T.

: Global Warming – a complete briefing (Cambridge

University Press)

4. Twidell, J & Weir, J. : Renewable Energy Resources (Elbs, 1988)

5. Wieder, S.

: An Introduction to Solar Energy for Scientists and Engineers

(John Wiley, 1982)

6. Keshavamurty, R.N. & Shanker Rao, M. : The Physics of Monsoons (Allied Publishers, 1992)

7. Haltiner, G.J. & Williams, R.T. : Numerical Weather Prediction (John Wiley, 1980)

8. Salby, M.L. : Fundamentals of Atmospheric Physics (Academic Press,1996)

9. Vallace, J.M. & Hobbs, P.W. : Atmospheric Science: An Introductory Survey (Academic

Press, 1977).

OLD (2017-18)


Soft Matter Physics



Lectures: 48

Tutorials: 08

Unit I: Introduction to soft matter systems

Classification in terms of their thermal, mechanical and unusual physical properties, Liquid crystals,

colloidal systems, biological membranes, macromolecules, Numerical methods for studying soft matter:

Lattice models, Coarse grain models, Gaussian overlap potential, Ellipsoidal contact potential.

Unit II: Liquid Crystals

Structure and classification of mesophases, Molecular theories of nematic and smectic liquid crystals,

Symmetry and order parameter, Phase identification with differential scanning calorimetry, Kinds of

liquid crystalline order: Structural and chemical standpoint, Landau’s theory of phase transition,

Generalization of Landau’s theory to liquid crystals, Polymer liquid crystals, Dielectric and electro-optical

properties, Ferroelectric liquid crystals (introduction only), Liquid crystal based applications.

Unit III: Colloidal systems and biological membranes Dispersion colloids: Stability, Fluctuations and forces, DLVO-theory, gels, emulsions and foams,

Association colloids: amphiphiles, micelles and critical micelle concentration in colloidal solution,

lyotropic liquid crystals, biological systems. Biological membranes: Bilayer properties, Chain rotational

isomerism, Marcelja’s molecular field theory, Even-odd effect, Phase diagram.

Unit IV: Macromolecules Polymer: Terminology and nomenclature, Polar masses and distributions, Chain-dimensions and

structures, Random walk polymer, self-avoiding random walk polymers, polymer solutions.

DNAs: Flory’s model of DNA condensation, Polymorphism of liquid crystal states by low molecular mass

double stranded DNA complexes, DNA condensation in water-polymeric solution, biological activity. Gel

electrophoresis, Reptation model, Gene therapy.

Books Recommended: 1. de Gennes, P.G. : Physics of Liquid Crystal (Clarendon Press (Oxford

University Press)

2. Collings, P. J. and Hard, M. : Introduction to Liquid Crystals (Taylor and Francis)

3. Hamley, I. W. : Introduction to Soft Matter (John Wiley and Sons

Ltd.)

4. Chandrasekhar, S. : Liquid Crystals (Cambridge University Press)

5. Lagerwall, S. T. : Ferroelectric and Antiferroelectric Liquid Crystals

(Wiley-VCH)

6. Allen, M. P. and Tildesley, D. J. : Computer Simulation of Liquids (Clarendon Press

(Oxford University Press))

7. Yevdokimov, Y.M., Salyanov, V.I.,

Semenov, S.V. and Skuridin, S.G.

: DNA Liquid Crystalline Dispersions and

Nanoconstructions (CRC Press)

8. Cevc, G. and Marsh D. : Phospholipid bilayers: Physical Principles and Models

(Wiley)

9. Jones, R.A.L. : Soft Condensed Matter (Oxford)

10. Gelbart, Roux and Ben-Shaul Micelles, Membranes, Micremulsions and Monolayers

(Springer)

(BOS: 21.05.18)


Soft Matter Physics

Paper Code: PHM-


Lectures: 48

Tutorials: 08

Unit I: Introduction to Soft Matter Systems

What is soft matter? Classification in terms of their thermal, mechanical and unusual physical properties,

Liquid crystals, Colloidal systems, Biological membranes, Macromolecules, Numerical methods for studying

soft matter: Lattice model and Gaussian overlap model.

Unit II: Liquid Crystals

Structure and classification of mesophases, Statistical theories of the nematic order, Symmetry and order

parameter, Phase identification with differential scanning calorimetry, Kinds of liquid crystalline order:

Structural and chemical standpoint, Generalization of Landau’s theory to liquid crystals, Polymer liquid

crystals, Dielectric and electro-optical properties, Ferroelectric liquid crystals (introduction only), Liquid

crystal display (LCD).

Unit III: Colloidal Systems and Biological Membranes Dispersion Colloids: Stability, Fluctuations and forces, DLVO-theory, gels, emulsions and foams.

Association Colloids: Amphiphiles, Micelles and critical micelle concentration in colloidal solution,

Lyotropic liquid crystals, Biological systems. Biological Membranes: Elastic properties of layered phases,

Vesicles, Phase diagram.

Unit IV: Macromolecules Polymer: Terminology and nomenclature, Molar masses and distributions, Chain-dimensions and structures,

Random walk polymer, Self-avoiding random walk polymers, Polymer solutions.

DNAs: Flory’s model of DNA condensation, Polymorphism of liquid crystal states by low molecular mass

double stranded DNA complexes, DNA condensation in water-polymeric solution, Biological activity. Gel

electrophoresis, Gene therapy.

Books Recommended:

1.

de Gennes, P.G.

:

Physics of Liquid Crystal (Clarendon Press (Oxford

University Press))

2. Singh, S. : Liquid Crystals Fundamentals (World Scientific)

3. Collings, P. J. and Hard, M. : Introduction to Liquid Crystals (Taylor and Francis)

4. Hamley, I. W. : Introduction to Soft Matter (John Wiley and Sons

Ltd.)

5. Chandrasekhar, S. : Liquid Crystals (Cambridge University Press)

6. Doi, M. : Soft Matter Physics (Oxford)

7. Yevdokimov, Y.M., Salyanov, V.I.,

Semenov, S.V. and Skuridin, S.G. : DNA Liquid Crystalline Dispersions and

Nanoconstructions (CRC Press)

8. Jones, R.A.L. : Soft Condensed Matter (Oxford)

9. Gelbart, Roux and Ben-Shaul : Micelles, Membranes, Micremulsions and

Monolayers (Springer)

Syllabus for M.Sc. , Semester-IV

OPEN ELECTIVE: ELEMENTS OF MODERN PHYSICS


(Credits: Theory-04) Theory: 48 Lectures,

Tutorials:08

Unit-I: Properties of Particle and Waves

Particle Properties of Waves :Blackbody radiation, Ultraviolet Catastrophe, Planck Radiation Formula.

Photoelectric effect, Compton effect, pair production, pair annihilation, Photon Absorption, linear

attenuation coefficient, photons and gravity: Photon ―mass, Photon energy after falling through height H.

Gravitational red shift. black hole Schwarzschild Radius, Black Holes.

Wave Properties of Particles: De Broglie waves: De Broglie wavelength, wave function, probability

density, De Broglie phase velocity, phase velocity and group velocity, particle diffraction, Davisson-

Germer experiment, particle in a box, uncertainty principle.

Unit-II: Quantum Mechanics

Review: Wave Function, Normalization, Well-Behaved Wave Functions, Probability. Schrödinger’s

equation: time-dependent form, Free particle, expectation value. Operators. Eigenvalues and

eigenfunctions. Finite potential well. Harmonic oscillator. Electron spin. Exclusion principle. Zeeman

effect.

Unit-III: Atoms and Molecules Atomic Structure, energy levels and spectrum of hydrogen. Nuclear Motion. Ionization energy. Spin-

orbit coupling, total angular momentum, ls coupling, x-ray spectra, auger effect, molecular bond,

electron sharing. Rotational energy levels, rotational spectra. Vibrational energy levels, vibrational

spectra. Electronic spectra of molecules, fluorescence, phosphorescence.

Unit- IV: Solids

Crystalline and amorphous solids, ionic crystals, covalent crystals, van der waals bond, metallic bond. X-

ray and bremsstrahlung radiation. X-ray diffraction, Bragg's law, X-ray diffractometer. Band theory of

solids: conductors, semiconductors, insulators, impurity semiconductors. Semiconductor devices: junction

diode, photodiodes, tunnel diode, zener diode, junction transistor, field-effect transistor.

Superconductivity: magnetic effects, Josephson junctions. Electron Microscopes,

Reference Books:

Concepts of Modern Physics, Arthur Beiser, 2002, McGraw-Hill.

Introduction to Modern Physics, Rich Meyer, Kennard, Coop, 2002, Tata McGraw Hill

Introduction to Quantum Mechanics, David J. Griffith, 2005, Pearson Education.

Physics for scientists and Engineers with Modern Physics, Jewett and Serway, 2010, Cengage

Learning.

Quantum Mechanics: Theory & Applications, A.K.Ghatak & S.Lokanathan, 2004, Macmillan

M.Sc. (Physics) IV Semester

General Lab. IV


1. To verify inverse square law and to measure total attenuation coefficients for gamma

radiation in different materials using end window G.M. counter.

2. To study velocity of ultrasonics in transformer oil by the method of diffraction grating

and to calculate grating element.

3. To determine slit width and slit separation using double slit diffraction and to verify

these measurements using microscope.

4. To study digital IC trainer logic circuits 4-bit digital comparator, full adder, J.K. flip-

flop and up/down counter.

5. To measure the ionization produced by charged particles having relative velocities,

0.3 < < 0.7 AND > 0.7

6. (a) To measure the intensity distribution of the Fraunhofer diffraction pattern of a single slit

and to verify Krichhoff’s diffraction formula.

(b) To calculate the uncertainty momentum from the diffraction pattern of single slits of

different widths and to confirm uncertainty principle.

7. To determine the gamma ray absorption coefficients for different gamma ray energies

using the Nal(TI) gamma ray spectrometer.

8. To perform arithmetic and logic operation on two 4-bit binary number using ALU

(74181).

9. To study the Stefan’s law using black body radiator.

M.Sc. (Physics) IV Semester

Elective Lab- II (2 credits): Condensed Matter Physics


1. Study the variation of dielectric constant of the given material as a function of frequency

using LCR bridge.

2. Determine the temperature dependence of Hall coefficient for a given sample.

3. Determine the resistivities of a given sample in absence and presence of magnetic field

and hence study the variation of magneto-resistance as a function of magnetic field.

4. Study the crystal structure of LiF single crystal using Laue’s method.

5. Record the x-ray diffraction pattern of a given material and estimate the crystallite size

using Scherrer equation.

6. (i) Determine the I-V and P-V characteristics of photovoltaic (PV) module.

(ii) Determine the I-V characteristics of series and parallel combination of PV module.

(iii) Show the effect of shading on module output power.

(iv) Find the fill factor of PV module.

M. Sc. IV – Semester

Elective Lab- II (2 credits): Electronics-B Paper Code: PHM-4074

1. (a) To study variation of voltage along an artificial transmission line in case of open-

circuited and short-circuited line at distant end.

(b) To plot load resistance versus power absorbed and determine characteristic resistance of

the line.

(c) To plot variation of voltage along the line for load equal to the characteristic resistance.

2. To study amplitude modulation using XR-2206

(a) for different frequencies and

(b) for different amplitude.

3. (a) To verify truth table of 4-to-1 line multiplexer (IC 74153).

(b) To implement any three variable truth table using above multiplexer.

(c) Using decoder (IC 74138) and four input NAND Gate (IC 7420), verify the same three

variable truth table.

4. Design the Wien’s bridge oscillator at different oscillating frequencies using Pspice (1

KHz, 10 KHz, 100KHz and 1 MHz).

5. To draw the characteristics of the following using Pspice :

(a) Output characteristics of NPN-BJT (2N2222).

(b) V-I characteristics of diode.

(c) Output characteristics of an N-Channel JFET.


Elective Lab- II (2 credits) : Atomic, Molecular and Optical Physics Lab-B


1. Determination the size of micro-particle using diode laser.

2. Dispersion curve for medium quartz spectrograph.

3. (a) Study of intensity distribution of diode laser beam .

(b) Determination of spot size and divergence angle of laser beam.

4. Determination of constituent elements in an alloy spectrum on 1.5m grating spectrograph.

5. Recording and analysis of copper spectrum.

6. Measurement of Raman spectrum of CCl4.


Elective Lab- II (2 credits): Electronics-B

1. (a) To study variation of voltage along an artificial transmission line in case of open-circuited and

short-circuited line at distance end.

(b) To plot load resistance versus power absorbed and determine the characteristics resistance of the

line.

(c) To plot variation of voltage along the line for load equal to the characteristics resistance.

2. To study amplitude modulation using XR-2206

(a) for different frequencies and

(b) for different amplitude.

3.(i) To verify truth table of 4-to-1 line multiplexer (IC 74153).

(ii) To implement any three variable truth table using above multiplexer.

(iii) Using decoder (IC 74138) and four input NAND gate (IC 7420), verify the same three variable

truth table.

4. Design the Wien’s bridge oscillator at different oscillating frequencies, using Pspice (1 KHz,

10KHz, 100KHz and 1 MHz).

5. To draw the characteristics of the following using Pspice:

(a) Output characteristics of NPN-BJT (2N2222).

(b) V-I characteristics of diode.

(c) Output characteristics of an N-channel JFET.

Syllabus for M.Sc. (Physics) Semester-I Mathematical ... · Syllabus for M.Sc. (Physics) Semester-I...

Documents

Transcript of Syllabus for M.Sc. (Physics) Semester-I Mathematical ... · Syllabus for M.Sc. (Physics) Semester-I...