Post Graduate Syllabus Department of Physics

Alipurduar University

Choice-based Credit System

Introduced from the Academic Session 2020-2021

Orientation of courses in four semesters for M.Sc in Physics

1st Semester

Subject

Code

Subject Marks Credits

PHY 101 Mathematical Physics 100 4(3+1)

PHY 102 Classical Mechanics and

special theory of relativity

100 4(3+1)

PHY 103 Electronics 100 4(3+1)

PHY 104 Laboratory Course-I

(Computational methods in

Physics)

100 4(3+1)

Theoretical-300

Practical -100

400

16

2nd Semester

Subject

Code

Subject Marks Credits

PHY 201 Quantum Mechanics-I 100 4(3+1)

PHY 202 Electrodynamics and Plasma

Physics

100 4(3+1)

PHY 203 Statistical Mechanics 100 4(3+1)

PHY 204 Laboratory Course-II

(Electronics)

100 4(3+1)

Theoretical-300

Practical -100

400

16

3rd Semester

Subject

Code

Subject Marks Credits

PHY 301 Nuclear and Particle Physics 100 4(3+1)

PHY 302 Condensed Matter Physics 100 4(3+1)

PHY 303 Quantum Mechanics-II 100 4(3+1)

PHY 305 Laboratory Course-III

(General Course )

100 4(3+1)

Theoretical-300

Practical -100

400

16

4th Semester

Subject

Code

Subject Marks Credits

PHY 401 Atomic and Molecular Physics 100 4(3+1)

PHY 402 Special Paper(Theory) 100 4(3+1)

PHY 403 Project on Special Paper 100 4(3+1)

PHY 404 Laboratory Course-IV

(Special Paper Practical)

100 4(3+1)

Theoretical-300

Practical -100

400

16

Special Papers- Group-A: Astrophysics and Cosmology, Group-B: Plasma Physics, Group-C

Laser and Nonlinear Optics.

Semester-wise marks distribution

Semester-I

Sl.

No

Paper Written Class

Test

Seminar Attendance Total Credits

1 101 75 10 10 5 100 4

2 102 75 10 10 5 100 4

3 103 75 10 10 5 100 4

Sl.

No

Paper Practical

Viva-

voce

Laboratory

Note Book

Total Credits

4 104 75 15 10 100 4

Semester-II

Sl.

No

Paper Written Class

Test

Seminar Attendance Total Credits

1 201 75 10 10 5 100 4

2 202 75 10 10 5 100 4

3 203 75 10 10 5 100 4

Sl.

No

Paper Practical Viva-

voce

Laboratory

Note Book

Total Credits

4 204 75 15 10 100 4

Semester-III

Sl.

No

Paper Written Class

Test

Seminar Attendance Total Credits

1 301 75 10 10 5 100 4

2 302 75 10 10 5 100 4

3 303 75 10 10 5 100 4

Sl.

No

Paper Practical Viva-

voce

Laboratory

Note Book

Total Credits

4 304 75 15 10 100 4

Semester-IV

Sl.

No

Paper Written Class

Test

Seminar Attendance Total Credits

1 401 75 10 10 5 100 4

2 402 75 10 10 5 100 4

Sl.

No

Paper Project/Thesis Viva-

voce

Presentation Total Credits

3 403 75 10 15 100 4

Sl.

No

Paper Practical Viva-

voce

Laboratory

Note Book

Total Credits

4 404 75 15 10 100 4

Salient features of the PG syllabus:

1. Total marks allotted to all papers in M.Sc. in Physics Examination will be

1600(equivalently,64credits), distributed equally in four semesters (400 ×4) or

(16credits× 4).

2. There will be three theoretical paper and one practical paper in first three Semesters.

In last Semester there will be two theoretical paper (one general and one special paper),

one practical paper (on special paper) and one project paper (on special paper).

3. Special papers to be offered at present will be: Astrophysics and Cosmology, Plasma

Physics and Laser and Nonlinear Optics- in Semester IV.

4. In each theory paper the end semester examination (ESE) of Semester I, II, III &IV

will be conducted over a total marks of 75(3 credits) of three hoursduration, while

continuous evaluation (CE) will be made over 25 marks (1 credit). Laboratory courses in

Semester I, II, III &IV(including special paper) and Project (on special paper in Semester

–IV) will be evaluated over 100 marks (4 credits).

5. The marks / grade obtained by a candidate in each paper/course should bedetermined

after taking into account the marks / grade obtained by the candidatein ESE and CE

together.

6. The detailed distribution of the marks in each papers are given above.

Semester-I

PHY 101: Mathematical Physics

A. Complex Analysis

Functions of a complex variable. Differentiability. Cauchy-Riemann equations.

Harmonic functions. Analytic functions. Entire functions. Multiple-valued functions.

Singular functions: poles and branch points; order of singularity; branch cuts.

Riemann surfaces. Complex integration. Contour integrals. Darboux inequality.

Cauchy’s theorem and consequences. Cauchy’s integral formula. Liouville’s theorem.

Morera’s theorem. Proof of Taylor and Laurent series. Expansion of functions about

regular and singular points. Residue theorem. Jordan’s lemma. Application of residue

theorem to the evaluation of definite integrals and the summation of infinite series.

Integrals involving branch point singularity. Analytic continuation. Schwarz reflection

principle.

B. Differential Equations, Special Functions & Integral Transforms:

Differential equations: Separation of variables for second order partial differential

equations and its application in solving the physical problems. Series solution of

linear second order differential equations. Legendre, Bessel, Hermite and confluent

hypergeometric equations. Dirac’s delta functions. Gamma and Beta functions.

Legendre and associated Legendre polynomials – spherical harmonics. Hermite and

Laguerre polynomials.

Integral Transforms: Fourier and Laplace transforms. Inverse transforms.

Covolution theorem. Solution of ordinary and partial differential equations by

transform methods.

Green’s Function: Green’s functions for ordinary and partial differential equations of

mathematical physics.

C. Linear Vector Space and Matrices

Linear Vector Space: Axiomatic definition. Basis and dimension of a vector space.

Inner product. Metric spaces. Cauchy-Scwartz inequality. Linear independence and

orthogonality of vectors, Gram-Schmidt orthogonalisation procedure. Linear

operators. Inverse of an operator. Dual spaces and adjoint operators. Special linear

operators. Projection operator.

Matrices: Matrix representation of linear operators. The algebra of matrices. Special

matrices. Rank of a matrix. Linear transformations. Change of basis. Eigenvalues and

eigenvectors of matrices. The Cayley-Hamilton theorem. Diagonalisation of matrices.

Functions of matrices. Bilinear and quadratic forms. Principal axis transformation.

Solution of linear equations by matrix method. Commuting matrices with degenerate

eigenvalues; Orthonormality of eigenvectors.

D. Tensor Analysis

Coordinate transformations. Scalars. Covariant, contravariant and mixed tensors.

Outer product. Inner product. Contraction. Symmetric and antisymmetric tensors.

Quotient law. Kronecker delta, Levi-civita symbol and metric tensors. Conjugate

tensor. Length and angle between vectors. Associated tensors. Raising and lowering

of indices. The Christoffel symbols and their transformation laws. Covariant

derivative of tensors.

E. Elements of Group theory

Definitions and examples. Order of a group. Group multiplication table.

Rearrangement theorem. Discrete and continuous groups. Isomorphism and

homomorphism. Illustrations with point symmetry groups.

Group representations: Faithful and unfaithful representations; Reducible and

irreducible representations. Schur’s lemma. Great orthogonality theorem and its

geometrical interpretation. Rotation groups. Unitary groups. Lie groups and Lie

algebra with SU(2) as an example.

Books Recommended:

1. M. R. Spiegel: Theory and Problems of Complex Variables (Schaum’s outline series).

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

3. J. Mathews and R. I. Walker: Mathematical Methods of Physics (Benjamin).

4. P. Dennery and A. Krzywicki: Mathematics for Physicists (Harper and Row).

5. L. Andrews and B. Shivamoggi,: Integral Transforms for Engineers (PHI).

6. A. Joshi: Matrices and Tensors (Wiley Esstern).

7. M. Tinkham: Group Theory and Quantum Mechanics (McGraw-Hill).

8. A. Joshi: Group Theory (Wiley Eastern).

9. F. Cotton: Chemical Applications of Group Theory (Wiley Eastern).

10. T. Dass and S. Sharma: Mathematical Methods in Classical and Quantum Physics

(Universities Press).

11. W. Tung: Group Theory in Physics (World Scientific).

PHY 102: Classical Mechanics and Special Theory of Relativity

A. Lagrange’s and Hamilton’s Principle

Principle of virtual work and D’ Alembert’s principle; constraints, generalized

coordinates and Lagrange’s equation of motion—applications. Principle of least

action. Hamilton’s principle—applications. Symmetry and conservation rules.

B. Two-body Central Force Problem

Central force, definition and characteristics; effective potential technique; graphical

analysis.

C. Hamilton’s equations

Legendre transformation and Hamilton’s canonical equations; Canonical equations

from a Variational principle and Routh’s procedure.

D. Canonical Transformations

Equation of canonical transformation; generating functions; Lagrange and Poisson

brackets; canonical invariance of Poisson brackets; equation of motion in Poisson

brackets notation; infinitesimal canonical transformation and constants of motion.

Angular momentum Poisson bracket relations.

E. Hamilton Jacobi theory

Hamilton-Jacobi equation, separation of variables; Hamilton’s principle and

characteristic functions; Action angle variables.

F. Small oscillations

Stable and unstable equilibria; small oscillations; vibration and normal co-ordinates.

G. Continuous systems

Transition from a discrete to a continuous system; Lagrangian formulation of

continuous systems and fields; Hamiltonian formulation—applications.

H. Rigid bodies

Independent coordinates; orthogonal transformations and rotations (finite and

infinitesimal); Euler angles; Inertia tensor and principal axis system; Euler’s equations;

Heavy symmetrical top.

I. Special Theory of Relativity

Lorentz transformations: Minkowski Space, Relativistic formulation of equation of

motion: Minkowski equation of motion; 4-vectors: velocity 4-vector, acceleration 4-

vector, energy-momentum 4-vector, force 4-vector; Tensors, Transformation properties,

Metric tensor, Raising and lowering of indices; Covariant equations of motion;

Lagrangian and Hamiltonian of a relativistic particle.

Books Recommended:

1. Classical Mechanics – H. Goldstein, C. Poole & J. Safko

2. Classical Mechanics, Vol. II – E. A. Desloge

3. Classical Mechanics – N. C. Rana & P. S. Joag

4. Mechanics – Landau &Lifshitz

5. Classical Mechanics – S. N. Biswas

6. Special Relativity – R. Resnick

7. Special Theory of Relativity – Banerjee & Banerjee

PHY 103: Electronics

A. Physics of Semiconductor devices

Metal semiconductor junctions – Schottkybarriers; Rectifying contacts; Ohmic

contacts; semiconductor devices –Tunnel diode; Photodiode; Gunn diode; IMPATT

diode;Solar cell; LED; LDR; p-n-p-n switch, SCR; Unijunction transistor (UJT).

B. Amplifiers:

Feedback in amplifiers

General properties of feedback amplifiers, types of feedback and their effect on

impedance levels. Practical feedback amplifiers using BJT, FET and OP-AMP.

Audio Power Amplifiers

Audio power amplifier requirements, Class A, Class Band Class C power amplifiers,

Push pull amplifiers.

C. Oscillators

Feedback sinusoidal oscillator and condition of oscillation, Phase-shiftoscillator,

Wien bridge oscillator and Multivibrator using BJT/FET; Negativeresistance

oscillator.

D. Power supplies and Electronic regulators

Linear Power supply, Electronicvoltage regulators, variable voltage supplies

using SCR, IC etc.

E. OP AMP

Differential amplifiers, DC and AC analysis, CMRR, constant currentbias level

translator. Block diagram of a typical OP-AMP circuit: Open-loopconfiguration.

Inverting and non-inverting amplifiers. OP AMP with negativefeedback - voltage

series feedback. Effect of feedback on closed loop gain, inputresistance, output

resistance, bandwidth, offset voltage and current, voltage follower.

F. Mathematical Operations

DC and AC amplifier, circuits for summing, scaling,integrator and differentiator, log,

antilog and other mathematical operations. Solutionof second-order differential

equations.

G. Special circuits using OP AMP

Comparators, square wave and triangle wavegenerators, voltage regulators, fixed and

adjustable voltage regulators, switchingregulators.

H. Digital Electronics

Number system and codes, logic gates, Boolean algebra; Logic simplification using

Karnaugh maps; SOP and POS design of logic circuits; Don't care conditions, five

and six variable K-maps. MUX as universal buildingblock. Adder, RCA, CLA and

BCD adder circuits; ADD-SHIFT and array multiplier circuits. RS, JK and MS-JK

flip-flops; registers and counters.

I. Networks and lines

Mesh and node analysis, network impedances, networktheorems. Resonant circuits,

inductively coupled circuits, reflected impedance, Passivefilter circuits, Propagation

constant; Constant-K low pass and high pass filters; Activefilters: Butterworth filters,

low pass and high pass filters;Butterworth polynomials; RCband pass filters; Band

reject Filter; Delay equalizer.

Books Recommended

1. Electronics fundamentals and application: John D. Ryder

2. Hand book of Electronics: Gupta and Kumar

3. Electronic Principles:Malvino

4. Principles of Electronics: Mehta and Mehta

5. Networks lines and fields: John D. Ryder

6. Solid state electronic devices: G. Streetman

7. Physics of semiconductor Devices: S. M. Sze

8. Electronic circuits and systems: Y. N. Bapat

9. Integrated Electronics: Millman and Halkias

10. Electronics fundamentals and application: Chattopadyay and Rakshit

11. Electronics (Classical and modern): R. Kar

12. Fundamentals of digital circuit: Anand Kumar

PHY 104: Laboratory Course-I (Computational methods in Physics)

A. Introduction to Computer Programming

Instructions to a computer, machine language, high level language, Programming

Concepts, different programming languages; Interpreter and compiler; Basic of

Python/Fortran/Matlab/Scilab/C/C++, Numbers, Variables, Comparison and Logic,

Strings, Lists, tuples and Loops, Control Flow, reading, writing and appending data

files

B. Approximations and errors in computing

Introduction, data errors, round off errors, truncation errors, modelling errors,

significant digits, absolute and relative errors, general formula of errors, error

estimation.

C. Operations with Matrices and Vectors

List and Arrays, Slicing out Rows and Columns from a Matrix, Arrays and Matrix

Arithmetic’s, Matrix Operations, Eigen Values and Eigen Vectors of Matrices

D. Interpolation

Newton's formulae, Lagrange's interpolation, inverse interpolation, Numerical

differentiation and integration: Numerical differentiation; numerical integration -

Simpson's and trapezoidal rules, Gauss' quadrature formula, accuracy of quadrature

formulas.

E. Solutions of algebraic, transcendental and linear simultaneous equations

Systems of Linear Equations, Nonlinear Equations: Bisection method; method of

regulafalsi, Newton-Raphson method, Secant method, Method of iteration;

Simultaneous equations, roots of a polynomial, Synthetic division method, Bairstow's

method for complex roots, Gauss Elimination Method, Gauss-Jordan Method; LV

Decomposition Method, Matrix Inversion Method, Round off of Errors and

Refinement, Method of Iteration.

F. Numerical Solution of Ordinary Differential Equations (ODE)

Introduction, Euler and Runge-Kutta Method, Solution of 2nd order differential

equations.

G. Numerical Solution of Boundary Value Problems

Shooting Method, Finite Difference Method, Eigen Value Problems, Time

Independent Schrodinger Equation

H. Random numbers

Properties of Random Numbers, Generation of Random Numbers and Monte Carlo

evaluation of integrals. Uniformly distributed, exponentially distributed and Gaussian

distributed random numbers, Integrations having finite and infinite limits.

I. Methods of least squares

Fitting of Experimental data, Least Squares Method, Fitting of Linear, Polynomial

and Transcendental Equations.

J. Statistics

Distribution functions, Moments of a distribution, Correlation function

K. Numerical Complex Analysis

Assignment of Complex Numbers, Numerical Complex Differentiation, Numerical

Complex Integration, Finding Roots of a Complex Equation, Calculation of Real

Improper Integrals

L. Fourier Series and Fourier Transform

Fourier Series, Discrete Fourier Series, Fourier Transform, Discrete Fourier

Transform, Fast Fourier Transform

List of Physics Practicals:

1. Simulation of Simple Pendulum and Damped Simple Pendulum

2. Simulation of the chaotic motion of double Pendulum.

3. Calculating the motion of a sphere falling under the influence of gravity and Stokes

drag.

4. Solution of one dimensional Stationary Heat Equation.

5. Calculates and Plots the Electric Fields and Potentials around an arbitrary number of

Point Charges.

6. Calculating the Magnetic Field With Bio-Savart Law

7. Solving the time independent Schrödinger Equation in one dimension using matrix

diagonalisation for different potentials

8. Calculating the Eigen energies of the lowest states for a one dimensional double well

potential.

9. Simulation of one dimensional wave propagation for various different potentials.

10. Computing the size of Hydrogen atom using Monte-Carlo Integration.

11. Computing the Brownian motion and understanding its connection with Diffusion.

12. Computing the Internal Energy, Specific heat and Magnetisation in the 1D and 2D

Ising Model.

Books Recommended

1. Fundamentals of Computers V. Rajaraman.

2. Essential Python for the Physicist, Giovanni Moruzzi, 2020, Springer.

3. Computational Physics with Python, Mark Newman, University of Michigan, 2012.

4. Computational Physics (Problem Solving with Python), Rubin H. Landau, Manuel J.

5. Paez and Cristian C. Bordeianu, 2015 WILEY-VCH Verlag GmbH & Co. KGaA

6. Introduction to Python for Science and Engineering, David J. Pine, CRC Press Taylor

7. & Francis Group, 2019.

Semester-II

PHY 201: Quantum Mechanics-I

A. Vector spaces in quantum mechanics

Hilbert space, Kets, bras and operators, Base bras, kets and matrix representation, Hermitian

operator, Orthogonality, Completeness. Postulates of quantum mechanics, Observable and

results of its measurement, The generalized uncertainty relation, Non-commutating

observables, Complete set of commuting observables, Change of basis. Momentum and

parity operators, Unitary operators, Discrete and continuous bases, Coordinate and

momentum representations, Linear harmonic oscillator by operator method, Coherent states.

B. Quantum dynamics

Schrodinger, Heisenberg - interaction pictures and equations of motion, Schrodinger

equation coordinate and momentum representation, Evolution operator.

C. Eigenvalue Problems

One-dimensional problems:

Square well problem (E > 0); Delta-function potential; Double-δ potential; Application to

molecular inversion; Multiple well potential, Kronig-Penney model.

Three dimensional problems:

Three dimensional problems in Cartesian and spherical polar coordinates, Three-dimensional

bound state problems: particle in a box, central potentials, free particle solution in spherical

polar co-ordinates, orbital angular momentum, spherical oscillator, H-atom.

D. Angular momentum & Spin

Infinitesimal rotation, Generator of rotation, Commutation rules, Matrix representation of

angular momentum operators, Angular momentum algebra; Eigen values and Eigen

function; Raising and lowering operators; Spin: Pauli's spin- 1/2 matrices, Eigen spinors,

Electron in static magnetic field, Larmor Precession, Stern-Gerlach experiment for spin-

½ system, Electron in an oscillating magnetic field, addition of angular momenta,

Clebsch-Gordon coefficients.

E. Time independent perturbation theory

Rayleigh-Schrödinger expansion, Nondegenerate states, energy and state corrections in first

& second order, degenerate states, Application to one-electron system – Relativistic mass

correction, Spin-orbit coupling (L-S and j-j), Zeeman effect and Stark effect.

F. Variational Method

Rayleigh-Ritz theorem, Ground state of helium atom, Method of variation of coefficients,

hydrogen molecule.

G. The WKB Approximation

Eikonal approximation, semi-classical reduction of Schrödinger equation, WKB equation,

turning points and connection formulae, bound state solutions in the WKB approximation,

barrier penetration

Books Recommended

1. Introduction to Quantum Mechanics – D. J. Griffiths

2. Quantum Mechanics – S. N. Biswas

3. Quantum Mechanics, Vol. I & II – C. Cohen-Tannoudji, B. Diu & F. Laloe.

4. Quantum Mechanics, Vol. I & II – A. Messiah

5. Quantum Mechanics, Leonard I. Schiff, 3rd Edn. 2010, Tata McGraw Hill

PHY 202: Electrodynamics and Plasma Physics

A. Propagation of Electromagnetic Waves

Maxwell’s equations, Vector and scalar potentials -gauge transformations - Lorentz

gauge, Coulomb gauge, Propagation of electromagnetic waves in free space, non-

conducting and conducting media, reflection and transmission at the boundary of two

non-conducting media, reflection from a metal surface, propagation of electromagnetic

waves in bounded media, wave guides, TE and TM modes. rectangular and cylindrical

wave guides, resonant cavities.

B. Radiation from moving point charges

Lienard- Wiechert potentials, Fields due to a charge moving with uniform velocity,

Fields due to an accelerated charge, Radiation at low & high velocity, Larmor's formula

and its relativistic generalization, Radiation when velocity (relativistic) and acceleration

are parallel-Bremsstrahlung, Radiation when velocity and acceleration are perpendicular-

Synchrotron radiation, angular distribution of radiated power. Radiation from an

oscillating dipole, radiation from a linear antenna.

C. Scattering theory and Relativistic Electrodynamics

Thomson scattering, Scattering from a bound electron. Rayleigh scattering. Absorption of

radiation by a bound electron. Normal and anomalous dispersion. Lorentz

electromagnetic theory.

Review of special theory of relativity, Minkowski Four vectors, Four dimensional

Lorentz transformations, electromagnetic field tensor, covariance of Maxwell’s

equations, transformation of electric and magnetic fields under Lorentz transformations.

D. Basic concepts of Plasma and gas discharge Physics

Brief history of plasma physics, Plasma Parameters, Examples of plasmas, Debye

shielding, Quasi-neutrality, Criteria of Plasmas, Applications of Plasma Physics, Charged

particles in homogeneous and inhomogeneous magnetic fields, Adiabatic invariance of

flux through an orbit, Magnetic mirror, Plasma Generation: Breakdown characteristics in

gases, Paschen Curve, Types of Low Pressure dc discharges, Stable Glow Discharge,

The Negative Glow, The Positive Column.

E. Fluid Models

The Two-Fluid Model, Maxwell’s Equations, Concept of a Fluid Description, The

Continuity Equation, Momentum Transport, Shear Flows, Magneto-hydrostatics, Isobaric

Surfaces, Magnetic Pressure, Diamagnetic Drift, Magneto-hydrodynamics, The

Generalized Ohm’s Law, Diffusion of a Magnetic Field, The Frozen-in Magnetic Flux,

The Pinch Effect, Application: Alfven Waves and the Parker Spiral

Books Recommended:

1. Classical Electrodynamics, J. D. Jackson, John Willey, 2007.

2. Introduction to Electrodynamics, D. J. Griffiths, Prentice Hall India, 2009.

3. Classical Electrodynamics, Greiner, Springer, 1998.

4. Classical Electromagnetic Radiation, J. Marion, Academic Press, 2012.

5. Introduction to Plasma Physics and Controlled Nuclear Fusion, F. F. Chen, Springer,

2016

6. Plasma Physics, Alexander Piel, Springer, 2010.

7. Gas Discharge Physics, Y. P. Raizer, Springer, 1991.

PHY 203: Statistical Mechanics

A. Classical Statistical Mechanics

Objective of statistical mechanics. Central Limit Theorem. Macroscopic and

microscopic states, physical significance of number of microstates. Phase space,

phase points, ensembles and ensembles averages. Statistical equilibrium, condition for

statistical equilibrium and Transition from thermodynamics to statistical mechanics.

Ideal classical gas, thermodynamic functions, entropy and Gibb’s paradox, partition

function and grand partition function, relation to thermodynamic quantities phase

space, density of distribution (phase points). Liouville’s equation and

Liouville’stheorem. Microcanonical ensemble. Equipartition theorem, fluctuations,

ergodic & quasi-ergodic systems, equivalence of different ensembles. Maxwell-

Boltzmann distribution, applications, inadequacy of classical theory.

B. Ensembles Theory

The Canonical Ensemble: equilibrium between a system and heat reservoir, various

statistical quantities in the canonical ensemble, partition function, Helmholtz free

energy, the classical systems, internal energy fluctuations, Equipartition theorem and

Virial theorem, harmonic Oscillators, statistics of paramagnetism, thermodynamics of

magnetic systems, negative temperatures .

The Grand Canonical Ensemble: equilibrium between a system and a particle-

energy reservoir, system in a grand canonical ensemble, density and energy

fluctuations in the grand canonical ensemble, thermodynamic phase diagrams, phase

equilibrium and the Clausius- Clapeyron equation . Chemical potential of ideal gas.

Chemical equilibrium and Saha Ionisation Equation.

C. Quantum Statistics

Formation of Quantum Statistics: Idea of quantum mechanical ensemble. Statistical

and quantum mechanical approaches. Pure and mixed states. Density matrix for

stationary ensembles. Density matrix and the partition function of a system of free

particles. Application to a free particle in a box, and an electron in a magnetic field.

Density matrix for a beam of spin 1/2 particles. Construction of the density matrix for

different states (pure and mixture) and calculation of the polarization vector.

Theory of simple gases: an ideal gas in a quantum-mechanical microcanonical

ensemble, an ideal gas in other quantum –mechanical ensembles, statistics of the

occupation numbers, kinetic considerations, gaseous systems composed of molecules

with internal motion, chemical equilibrium

Ideal Bose system: Thermodynamic behaviour of an ideal Bose gas, Bose-Einstein

condensation in ultracold atomic gases, thermodynamics of blackbody radiation,

elementary excitations in liquid helium-II.

Ideal Fermi Systems: Thermodynamic behaviour of an ideal Fermi gas, magnetic

behaviour of an ideal Fermi gas, the electron gas in metals, ultracold atomic Fermi

gas, statistical equilibrium of white dwarf stars, statistical model of the atom

D. Phase Transition

Some applications: Specific heats of diatomic gases and crystalline solids; chemical

equilibrium; thermal ionization; imperfect gases.

Cluster and cluster integrals; The second viral coefficient; van der Wall's equation;

cluster expansion of the equation of state of real classical gas.

Irreversible processes: Onsager's relations; applications.

Strongly interacting systems: Ising model. Idea of exchange interaction and

Heisenberg Hamiltonian. Ising Hamiltonian as a truncated Heisenberg Hamiltonian.

Exact solution of one-dimensional Ising system (Matrix methods). Bragg-William’s

approximation (Mean field theory) and the Bethe-Peierls approximation.

Books Recommended:

1. R. K. Pathria, Statistical Mechanics

2. K. Huang, Introduction to Statistical Mechanics

3. Silvio R. A. Salinas, Introduction to Statistical Mechanics.

4. F. Reif, Fundamentals of Statistical and Thermal Physics.

5. Kadanoff, Statistical Mechanics. World Scientific.

6. R. Kubo, Statistical Mechanics. (Collection of problems)

7. Sanchez Bowley, Introductory Statistical Mechanics, Oxford University Press

PHY 204: Laboratory Course-II (Electronics)

(List of experiments should be regarded as suggestive of the standard and may not be

strictly adhered to. New experiments of similar standard may be added and old

experiments may be deleted whenever felt it necessary)

1. To design and construct a stabilized power supply (Constant Voltage Source)

usingdiscrete devices and to study the variation of load voltage with load current.

Show alsothe variation of load voltage with load current using IC 78XX.

2. To design and construct constant – K type (a) low pass (b) high pass (c) band

passfilters (using πsection) and to study the variation of attenuation and phase

constants ofthese filters with input frequency. To determine the cut off frequencies

and to comparewith theoretical values.

3. To study OPAMP as voltage regulator and show the variation of load voltage

withload current.

4. Studies on Diac, Triac and SCR.

5. To study the variation of output voltage with frequency and load resistance for agiven

class-B Push Pull amplifier and to obtain the variation of output power withfrequency

and load resistance.

6. To design and construct clipping and clamping circuits using diodes and to study

thevariation of output amplitude and wave form using CRO.

7. To design an astable multi vibrator using BJT and to study its output waveform

andfrequency for various RC values. To study how the output can be converted to a

squarewave using a Schmitt trigger or Zener diode.

8. To design a Uni-junction Transistor circuit and draw its characteristic curves

fordifferent values of supply voltage. Use it as a saw - tooth wave generator

anddetermine the frequency of oscillation.

9. To study the various feedback amplifier using OPAMP

i. Voltage series feedback amplifier (VCVS)

ii. Voltage shunt feedback amplifier (CCVS)

iii. Current series feedback amplifier (VCCS)

iv. Current shunt feedback amplifier (CCCS)

10. To study OP-AMP as voltage comparator and Schmitt trigger. Plot a curve in

inputand output voltages and show how the output switches from positive to negative

valuefor comparator.

11. To design and construct a Wein-Bridge oscillator using OPAMP and to study

itsoutput waveform and frequency for various RC values.

12. To study the various type of digital- to- analog (D/A) converters.

13. To construct Half-Adder and Full-Adder circuits using logic gates and to

performsome simple 2's complement Adder-subtractor operations (two decimal

digits).

Books Recommended:

1. Lab. Experiments and PSPICE Simulations in Analog electronics: L. K.Maheswary

and M.M.S. Anand

Semester-III

PHY 301: Nuclear and Particle Physics

A. Properties of nucleus

Nuclear size, shape and charge distribution, spin and parity, Magnetic dipole moment,

Electric quadrupole moment and nuclear shape, Anomalous magnetic moments of

nucleons and qualitative discussions about their origin.

B. Nuclear Models

Evidence of shell structure, Single-particle shell model, spin-orbit coupling; spin,

parity, quadrupole moment, and magnetic moment of nuclear ground states, validity

and limitations of shell model. Collective model, Vibrational and Rotational spectra.

C. Nuclear decays

Beta decay, Fermi's theory on beta decay, beta spectrum, selection rule, allowed and

forbidden transitions, parity violation, neutrino detection. Gamma decay, multipole

transition, angular momentum and parity selection rules, internal conversion, nuclear

isomerism.

D. Nuclear Interactions and Nuclear Reactions

Nuclear two body problem, The deuteron, simple theory, spin dependence, tensor

force, nucleon nucleon scattering, partial wave analysis of n-p scattering,

determination of phase shift, singlet and triplet potential, effective range theory, low

energy p-p scattering (qualitative discussion), Charge symmetry and charge

independence of nuclear forces. Isospin symmetry, Exchange interaction, Meson

theory of nuclear forces. Nuclear reactions- Different types of reactions, Quantum

mechanical theory, Principle of detailed balance, Compound nuclear reaction –

Ghosal's experiment.

E. Particle Accelerators and detectors

Betatron – principle and betatron oscillations, Principle of phase stability and phase

oscillations, Synchro-cyclotron, Synchrotron and Linear accelerators. Gas filled

detector-current vs applied voltage curve, Ionisation region, Proportional region, GM

region and spark region. Construction and working principle of GM counting system,

its advantages and limitations, scintillation detector and semiconductor detector.

F. Elementary particle Physics

Classification of fundamental forces - typical strengths and time scales. Elementary

particles and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.).

Symmetry, Conservation laws. Charge-conjugation, Parity and T reversal, CPT

theorem, Gell-Mann Nishijima formula, Quark model. Charm, beauty and truth,

gluons, Quark- Confinement. Gell-Mann-Okubo mass formula for octet and decouplet

hadrons.

Books Recommended:

1. Introductory Nuclear Physics, Kenneth.S. Krane, Wiley, 1987.

2. Nuclear Physics, S.N. Ghosal, S. Chand, 2008

3. Nuclear Physics: Theory and Experimental, H. S. Hans, New Age International, 2019.

4. Nuclear Physics: Theory and Experiment, R. R. Roy and B. P. Nigam, New Age

International, 1996.

5. Nuclear and Particle Physics: An Introduction, B.R. Martin, Wiley, 2006.

6. Concepts of Nuclear Physics, B. Cohen, McGraw-Hill, India, 2017.

7. Introduction to Elementary Particles, D Griffiths, Wiley-VCH, 2008.

PHY 302: Condensed Matter Physics.

A. Types of Bonding

The van der waals bond. Cohesive energy of inert gas solids. Ionic bond. Cohesive

energy and bulk modulus of ionic crystals. Medelung constant. The covalent bond.

Metallic bond.

B. Elementary Crystallography

Bravais lattices; unit cell, Wigner-Seitz cell, symmetry operations and classification

of 2-and 3-dimensional Bravais lattices,Crystal structures, basis, crystal class, point

group and space group (information only), simple crystal structures, reciprocal lattice

and Brillouin zone, reciprocal lattice for SC, BCC and FCC structures, x-ray

diffraction Bragg's law; Laue diffraction; atomic scattering factor; crystal structure

factor, Ewald construction, neutron diffraction; electron diffraction.

C. Dynamics of atoms in a crystal

Failures of the static model, Classical theory of lattice vibration under harmonic

approximation, the monoatomic and diatomic linear lattices, acoustical and optical

modes, high and low temperature specific heat, models of Debye and Einstein.

D. Free electron in Solids

Classical free electron theory; its failures; Fermi-Dirac probability distribution

function; periodic boundary conditions in a solid; density of states; Fermi energy-its

dependence upon temperature; electronic specific heat of solid; Paramagnetism of free

electrons.

E. Band theory

Bloch theorem;Kronig- Penney model; motion of electrons in a periodic lattice;

Brillouin zones for simple lattices; crystal momentum; effective mass; nearly free

electron approximation; tight binding approximation; application to simple cubic

lattices; ideas of Fermi surfaces; semi-classical dynamics of electrons in a band;

Landau levels - de Haas van Alphen effect.

F. Dielectric properties of Solids

Electronic, ionic, and orientational polarization; static dielectric constant of gases and

solids; Complex dielectric constant and dielectric losses, relaxation time, Debye

equations; Ferroelectricity, displacive phase transition, Landau theory of phase

transition.

G. Magnetic properties of solids

Origin of magnetism; Diamagnetism:quantum theory of atomic diamagnetism;Landau

diamagnetism (qualitative discussion); Paramagnetism: classical and quantum theory of

paramagnetism; case of rare-earth and iron-group ions; quenching of orbital angular

momentum; Pauli paramagnetism; Ferromagnetism: Curie-Weiss law, Heisenberg's

exchange interaction, Ferromagnetic domains - calculation of wall thickness and

energy; Ferrimagnetism and antiferromagnetism..

H. Semiconductors

General properties, effective mass- charge carrier density in intrinsic semiconductors

– statistics, doping, carrier density in doped semiconductors – impurity band

conduction, p-n junction, metal-semiconductor Schottky contact, important

semiconductor devices.

I. Superconductivity

Phenomenological description – critical temperature, persistent current, Meissner

effect; Thermodynamics of superconducting transition; The two-fluid model; London

equation; Type I and II superconductors; the BCS ground state (qualitative idea of

phononmediated pairing), Quantization of magnetic flux and Josephson effect, high

TC superconductor (informative only).

Books Recommended:

1. Introduction to Solid State Physics – Charles Kittel,

2. Solid State Physics – N.W. Ashcroft and N.D. Mermin,

3. Introductory Solid State Physics – H. P. Myers,

4. Elementary Solid State Physics – M. Ali Omar,

5. Crystallography applied to Solid State Physics – A. R.Verma& O.N. Srivastava

6. Solid State Physics – A. J. Dekker

PHY 303: Quantum Mechanics-II

A. Identical Particle

Two particle system, Wave function of Bosons and Fermions, Exchange operator,

symmetrisation requirement, Slater determinant, Exchange forces for the case of

distinguishable and Identical Particles, Pauli's exclusion principle, BE and FD

statistics.

B. Time-dependent perturbation theory

Time dependent perturbation theory, interaction picture; Constant and harmonic

perturbations — transition probability, Fermi’s Golden rule; Sudden and adiabatic

approximations, Interaction of an atom with electromagnetic Wave, Electric dipole

radiation.

C. Symmetries

Invariance principles and conservation laws, space and time translation, rotation,

infinitesimal and finite transformations, Rotation group, homomorphism between

SO(3) and SU(2), Explicit matrix representation of generators for j = 1/2 and j = 1,

Rotation matrices, Irreducible spherical tensor operators, Wigner-Eckart theorem,

discrete symmetries, parity and time reversal, Kramers degeneracy

D. Scattering theory

Differential and total scattering cross-sections, scattering amplitude; Scattering by

spherically symmetric potentials; Partial wave analysis and phase shifts; Ramsauer-

Townsend effect; Relation between sign of phase shift and attractive or repulsive

nature of the potential; Scattering by a rigid sphere and square well; Coulomb

scattering-Rutherford formula ; Formal theory of scattering — Green’s function in

scattering theory; Lippman-Schwinger equation; Born approximation.

E. Relativistic quantum mechanics

Klein-Gordon equation, Dirac equation and its plane wave solutions,

orthonormalization and completeness, spin and magnetic moment of an electron,

Feynman Stuckelberg interpretation of negative energy states and concept of

antiparticles, Large and small components, Pauli's theory as non-relativistic

approximation, higher order corrections, central potential, H-atom. Lorentz group,

transformation property of spinors, covariance of Dirac equation, construction of

covariant quantities.

F. Quantum Field Theory

Classical field theory, Hamiltonian Formalism, Conservation Laws-Noether’s

theorem, Non relativistic system with n degrees of freedom, Continuum limit, free

field quantization of non-relativistic limit,

Relativistic free fields- quantization of scalar and Dirac fields, Creation and

annihilation operators, Commutation relation, Fock space representation

Books Recommended:

1. Advanced Quantum Mechanics – J. J. Sakurai

2. Quantum Physics – S. Gasiorowicz

3. Quantum Mechanics – A. K. Ghatak& S. Lokanathan

4. Quantum Field Theory – F. Mandl& G. Shaw

5. E. Merzbacher: Quantum Mechanics.

6. F. Schwabl: Advanced Quantum Mechanics.

7. Y.V. Nazarov: Advanced Quantum Mechanics.

8. L. H. Ryder: Quantum Field Theory, Academic Publisher

9. S. J. Chang: Introduction to Quantum Field Theory, World Scientific

10. A. Lahiri and P.B. Paul: A first book on Quantum Field Theory, Narosa

PHY 304: Laboratory Course-III (General Course)

Physics General Lab:

1. To study of Electron Spin Resonance – determine magnetic field as a function of the

resonance frequency.

2. To study the Zeeman effect: with external magnetic field; Hyperfine splitting.

3. To measure the Dielectric Constant of a dielectric materials with frequency.

4. To determine the Hall coefficient of a semiconductor sample.

5. To draw the BH curve of Fe using Solenoid & determine energy loss from Hysteresis.

6. To measure the resistivity of semiconductor (Ge) with temperature by four-probe

method and to determine its band gap.

7. Determination of Lande g-factor by ESR spectroscopy.

8. To determine the wavelength and velocity of ultrasonic waves in a liquid (Kerosene

Oil, Xylene, etc.) by studying the diffraction through ultrasonic grating.

9. To study the characteristics curve of G.M. Counter and to study the decay of activity

of an artificially activated source.

10. To study the characteristics curve of G.M. Counter and to find out the gamma

counting efficiency of G.M. Tubes.

11. To study the characteristics curve of G.M. Counter and to study the gamma

absorption in Pb/Hg absorber.

12. To study the pulse height spectra of Cs-137 using a scintillator detector.

13. To measure the Magnetic susceptibility of Solids (Gouys Method).

Semester-IV

PHY 401: Atomic and Molecular Physics

A. One-Electron Atom

Quantum States; Atomic orbitals; H-atom spectrum, fine structure of H-atom, Lamb-

Rutherford experiment, Lamb shift, hyperfine structure.

B. Two-Electron Atom

Spectral terms, exchange degeneracy, singlet and triplet structure; LS, JJ and mixed

coupling schemes.

C. Many-Electron Atom

Independent particle model, central field approximation, Russel-Saunders coupling,

alkali spectra, fine and hyperfine structure in alkali spectra.

D. Interaction with External Fields

Time dependent perturbation treatment, electric dipole approximation, stimulated and

spontaneous emission, absorption coefficients, selection rules, line broadening.

Normal and anomalous Zeeman effect, Paschen-Back effect, Stark effect.

E. Laser

Basic elements of a laser, properties of laser light, spontaneous and stimulated

emission; Einstein coefficients, light amplification, population inversion and

threshold condition for laser oscillations; optical resonator models of a rectangular

cavity, rate equations: two-level, three-level systems. Temporal and spatial

coherences, line broadening, collision and Doppler broadening.Some laser systems:

Gas laser, Nd:YAG, Dye laser, Semiconductor laser, Excimer laser, Chemical laser,

laser applications: Holography and Optical communication.

F. Molecular Orbitals

Linear combination of atomic orbital, H-molecular ion, H-molecule, Heitler London

theory.

G. Molecular Spectra

Rotation of a diatomic molecule, rotational transition, selection rules, rotational

spectra of diatomic molecules as rigid rotor and as non-rigid rotors Stark effect in

molecular rotation spectra. Diatomic molecules as linear symmetric top and

asymmetric top. Vibration of diatomic molecules, harmonic oscillator, an-

harmonicity, selection rules, and spectrum, symmetry property of molecular

vibration, intensity of spectral lines. Rotation-vibration spectra of diatomic

molecules, PQR branching, Raman spectroscopy – pure rotational spectra and

vibrational spectra. Electronic spectra of diatomic molecules, Frank-Condon

principle. Born-Oppenheimer approximation, vibrational and rotational structure of

electronic transitions.

Books Recommended:

1. Atomic and Molecular Spectroscopy – M. C. Gupta

2. Atomic and Molecular Spectroscopy – Rita Kakkar

3. Molecular Spectra and Molecular Structure, Vol. I – G. Herzberg

4. Introduction to Molecular Spectroscopy – Raj Kumar

5. Lasers and Nonlinear Optics – B. B. Laud

6. Lasers: Theory and Applications – K. Thyagarajan& A. K. Ghatak

7. Laser and Fundamentals – W. T. Silfvast

PHY 402: Special Paper (Theory)

Group-A: Astrophysics and Cosmology

A. Celestial Co-ordinate system, Observational techniques and Telescopes

Celestial sphere- Sidereal and solar time, Equation of time-different co-ordinate

system, determination of luminosity, luminosity and magnitude of star relations with

mass, radius, colour index- distance determination by parallax and other methods.

Telescopes for γ-ray, X-ray, UV, IR, mm, radio and optical astronomy. Detector and

observatories for γ-ray, X-ray, UV, IR astronomy.

B. Physical Processes

Radiation Transfer. Equation of radiation transfer, Black-body/thermal radiation,

Opacity and optical depth, solution of radiation transfer equations in limiting cases,

Rosseland mean opacity. Ionisation losses, Thermal Bremsstrhlung emission,

syncroton emission. Self absorption and the emergent spectrum. Thomson scattering.

Compton and Inverse Compton scattering. Scattering in a region with magnetic field,

Faraday radiation, convection instability transfer of energy from cores to stars.

Supersonic motion, shocks. Magneto-hydrodynamics.

C. Star formation, Interstellar medium (ISM)

Various nebula, Jeans condition for collapse, Protostars, star formation. Stellar

Clusters: open and Globular, IMF. Variable stars, period luminosity relations and

distance determination, Binary stars, types of binaries.

D. Stellar structure and Evolution

Spectral classification of stars, Saha’ s equation, CNO cycles, HR Diagram,

radiative transfer, structure of spectral line, hydrostatic equilibrium, equation of

state, main sequence. Evolution of main sequence, late stages, supernovae

degenerate remnants: white dwarf, Chandrasekhar limit, Neutron star, pulsars,

Black Holes, γ-ray burst.

E. Sun and Solar system

Physical characteristics of sun-rotation, magnetic field, granulation, sunspots,

other chromospheric activities. Primordial Solar Nebula, Origin and evolution of

solar system, planets, comets, asteroids and other minor bodies, formation of

comets, Oort cloud planetary dust and gas.

F. Galaxies

The Milky way Galaxy, Kinematics, Hubble classification scheme for external

galaxies: spirals, elliptical, irregulars; Normal galaxies and AGNs, Quasi-stellar

objects, Unified model.

G. General Theory of Relativity

Principal of Equivalence, Gravity and Geometry, Metric Tensor and its properties,

Curved space time, Tensor calculus: co- variant differentiation, parallel transport,

Bianchi Identities, Particle trajectories in Gravitational field, Einstein’s Field

equations and Stress-energy tensor, Schwarzschild metric.

H. Stellar structure and Evolution

Hubble’s law, Friedman- Robertson- Walker Model, Cosmological constant,

Theories of origin and evolution of Universe, Standard Cosmological model,

Thermodynamics of early universe, Nucleo-synthesis, Microwave background

radiation, Elementary ideas on structure formations, age of Universe.

I. Astroparticle Physics

Dark Matter and Dark Energy, Probable compositions, Experimental detection,

Nature of Matter and Interaction at High Energies: Neutrino mass, Proton Decay,

Neutrino mixing, High Energy phenomena: Charged Particles, Gamma Rays,

Gamma ray bursts, Neutrino Astronomy, Gravitational Waves.

Books Recommended:

1. Astrophysics, K. D. Abhankar, Orient Longman.

2. Astrophysics, K. S. Krishnaswamy, C. U. P.

3. Text Book on Astronomy and Astrophysics with elements of cosmology, V. B.

Bhatia, Norosa.

4. Physical Universe, F. Shu, C. U. P.

5. Observational Astrophysics, Smith, C. U. P.

6. Astrophysical quantities, K. R. Lang, Springer Verlag.

7. Introduction to cosmology, J. V. Narlikar, C. U. P.

8. General Relativity and Cosmology, J. V. Narlikar, McMillan.

9. Astrophysics, K. S. Krishnaswamy, C. U. P.

10. The classical theory of Fields, Vol- 2, Landau and Lifshitz, Butterworth Heinemann.

11. Astrophysical quantities, K. R. Lang, Springer Verlag.

12. Physical Universe, F. Shu, C. U. P.

Group-B: Plasma Physics

A. Waves in Plasma

Plasma Oscillations, Electron Plasma waves, Ion acoustic Waves, Validity of Plasma

Approximation, Comparison of Ion and Electron waves, Electrostatic Electron

Oscillation and Ion acoustic wave perpendicular to B, The lower hybrid frequency,

Electromagnetic waves with B0=0, Experimental Applications, Electromagnetic

waves perpendicular to B0, Cut-offs and resonances, Electromagnetic waves parallel

to B0, Experimental consequences

B. Equilibrium and Stability

Hydro magnetic equilibrium, The concept of beta, Diffusion of Magnetic field into a

Plasma, Classification of Instabilities, Two-stream Instability, The Gravitational

Instability, Resistive drift waves

C. Kinetic Theory of Plasmas

The Vlasov Model, Derivation of Vlasov Equation, Properties of the Vlasov Equation,

Relation between the Vlasov Equation and Fluid Models, Plasma Oscillation and

Landau Damping, A Physical Picture of Landau Damping, Damping of Ion Acoustic

Waves

D. Plasma Boundaries and Nonlinear Plasma Effects

The Space-Charge Sheath, The Child-Langmuir Law, The Bohm Criterion, Langmuir

Probe, Ion acoustic shock waves, Parametric Instabilities, Plasma Echoes, Non-linear

Landau damping

E. Dusty Plasmas

Introduction, Examples of dusty plasmas, Charging of Dust Particles, Forces on Dust

Particles, Waves in Dusty Plasmas, Plasma Crystals

Books Recommended:

1. Introduction to Plasma Physics and Controlled Nuclear Fusion, F. F. Chen, Springer,

2016

2. Plasma Physics, Alexander Piel, Springer, 2010.

3. Fundamentals of Plasma Physics, J. A. Bittencourt, Springer, 2004.

4. Fundamental of Plasma Physics, P. M. Bellan, Cambridge University Press, 2006.

5. Gas Discharge Physics, Y. P. Raizer, Springer, 1991.

6. Principles of Plasma Discharges and Materials Processing, M. A. Lieberman and A. J.

Lichtenberg, John Wiley & Sons, Inc., 2005.

Group-C: Laser and Nonlinear Optics

A. Basics of Lasers and its applications

Properties of Lasers, Q-switching and mode locking techniques: Q-switching,

production of a giant pulse, methods of Q-switching: Mechanical shutters, electro-

optical shutters, acousto-optic Q- switches, shutter using saturable dyes. Mode

locking: Active and passive mode locking techniques, Materials processing with

lasers: Drilling, Cutting, and Welding, Nuclear fusing with lasers, Communication by

lasers, laser in astronomy and in medical field.

B. Introduction to nonlinear optical processes

Propagation of electromagnetic waves in non-linear optical media, Non-linear optical

susceptibilities and Symmetry.

C. Nonlinear Processes: Second and Third order nonlinear effects

Second harmonic generation (SHG), Phase matching techniques, Parametric

fluorescence, Parametric amplification, Three wave mixing, Sum and Difference

frequency generation, Parametric oscillation, Photo-refractive effect. Third harmonic

generation (THG), Self-phase modulation, Cross-phase modulation, Four wave

mixing, Optical phase conjugation, Kerr effect, Self-focusing and Self defocusing,

Stimulated Scattering: Rayleigh, Brillouin and Raman Processes.

D. Pulse propagation through third order nonlinear optical medium

Propagation in Fibers, Pulse Propagation in a Linear Dispersive Medium, Optical

Pulse Propagation in Nonlinear Medium, Solitons in Optical Fibers, Long Distance

Soliton Transmission System.

E. Quantum-mechanical description

Use of Density matrix and Perturbative approach to nonlinear optical susceptibilities.

Multiphoton processes. Theory of Two photon process, Experiment evidences of 2PA

materials, Three photon process, Z-scan technique to measure nonlinear properties.

Books Recommended:

1. Lasers: Theory and Applications, K Thyagarajan and A K Ghatak, Springer, 2010.

2. Laser and Fundamentals, W. T. Silfvast,Cambridge University Press, 2004.

3. Nonlinear Optics, R.W. Boyd, Academic press, Elsevier, 2008.

4. Laser and Nonlinear Optics; B. B. Laud, New Age, 1991.

5. Principles of Nonlinear Optics, Y. R. Shen, A Wiley Inter-science Publication, 1984.

6. Fundamentals of Nonlinear Optics, P. E. Powers, CRC Press, 2011.

7. Handbook of Nonlinear Optics, R. L. Sutherland, 2003.

PHY 403: Project on Special Paper

Topic of the projects will be decided in fourth semester.

PHY 404: Laboratory Course-IV (Special Paper Practical)

Group-A: Astrophysics & Cosmology

1. Designing and construction of optical telescopes.

2. Observation of galactic and extra – galactic objects using optical telescopes.

3. Observation of galactic and extra – galactic sources for X-rays, ϒ- rays using various

detectors.

4. Data analysis of different galactic and extra – galactic sources in different energy

bands using IRAF &HEASoft software.

Group-B: Plasma Physics

1. Experimental Study of Paschen Curve for a Given Gas.

2. To Study the condition of occurrence of striations in Low Pressure DC Discharges.

3. Plasma Diagnostic: Measurement of Plasma Parameters using Single Langmuir Probe.

4. Plasma Diagnostic: Measurement of Plasma Parameters using Double Langmuir

Probe.

5. Study of Launching and Detection of Ion Acoustic Waves and demonstration of

Collective Behaviour of Plasma.

Books Recommended:

1. Introduction to Plasma Physics and Controlled Nuclear Fusion, F. F. Chen,

Springer, 2016

2. Plasma Physics, Alexander Piel, Springer, 2010.

3. Fundamentals of Plasma Physics, J. A. Bittencourt, Springer, 2004.

4. Fundamental of Plasma Physics, P. M. Bellan, Cambridge University Press, 2006.

5. Gas Discharge Physics, Y. P. Raizer, Springer, 1991.

6. Principles of Plasma Discharges and Materials Processing, M. A. Lieberman and

A. J. Lichtenberg, John Wiley & Sons, Inc., 2005.

Group-C: Laser and Nonlinear Optics

1. To calculate the beam divergence and spot size of the given laser beam.

2. Determination of distance between two slits using interference of laser light through

double slit.

3. Determination of refractive index of glass and Perspex using total internal reflection.

4. Determination of refractive index of liquids using shift in the diffraction pattern.

5. Michelson interferometer experiment- Refractive index of glass plate

6. Michelson interferometer experiment- wavelength of laser beam.

7. Fabry-Perot interferometer experiment.

8. Numerical Aperture of Optical Fiber.

9. Simple experiments with lasers self-explaining Q-switching, SHG, Nonlinear

absorption and refraction.

10. pyNLO: Nonlinear optics modelling with Python.

11. Numerical model to solve pulse propagation in nonlinear medium with split step

Fourier method.

12. Simulations of laser physics experiments based on online virtual lab (using MHRD

web resource).