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SCHEME

M.Sc. Physics (Nano–Science & Technology) PART– I (I & II SEMESTERS) 2017 – 2018 SESSIONS

Code Title of Paper Hours (Per Week)

Max. Marks Examination Time (hrs)

SEMESTER – I Total Ext. Int.Core Papers

NT 1.1.1 Mathematical Physics 4 80 60 20 03

NT 1.1.2 Classical Mechanics 4 80 60 20 03

NT 1.1.3 Condensed Matter Physics

4 80 60 20 03

Elective Papers*

NT 1.1.4 (i) Analog Electronics(ii) Remote Sensing(iii) Microwave and its

Propagation

4 80 60 20 03

NT 1.1.5 Lab Practice: Electronics 9 120 90 30 03

NT 1.1.6 Computer Laboratory 3 60 45 15 03

SEMESTER – IICore Papers

NT 1.2.1 Quantum Mechanics 4 80 60 20 03

NT 1.2.2 Digital Electronics 4 80 60 20 03

NT 1.2.3 Fundamentals ofNanotechnology

4 80 60 20 03

Elective Papers*

NT 1.2.4 (i) Applied Optics(ii) Mathematical Physics

and Classical Mechanics

(iii) Computer Fundamentals and Programming with C++

(iv) Atomic and Molecular Spectroscopy

4 80 60 20 03

NT 1.2.5 Lab Practice: Laser-Optics

9 120 90 30 03

NT 1.2.6 Computer Laboratory 3 60 45 15 03

For Other Departments Students: Qualifying Paper in Semester -IIPAPER: Domestic Use of Electric Gadgets

NOTE: Only one Elective paper will be offered depending on the availability of staff.*

Semester– I

NT 1.1.1 MATHEMATICAL PHYSICS

Maximum Marks: External 60 Time Allowed: 3 Hours Internal 20 Total Teaching hours: 50 Total 80 Pass Marks: 35%

Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.

Use of scientific calculator is allowed.

SECTION A

Gamma and Beta functions: Definition and their relations

Bessel functions: Series solutions of Bessel's differential equation recurrence relations, Evaluation of Jn(x) for half-integral, generating function, Orthogonality (statement only).

Legendre Polynomials: Series solution of Legendre differential equation, Rodrigue and recurrence formulae, Generating function; Associated Legendre equation and polynomials;

Hermite polynomials: Series solution of Hermite differential equation, Hermite polynomials, Generating functions, Recurrence relations, Orthogonality (statement only), Simple integral involving Hermite polynomials.

Laplace transforms, Definition, Laplace transform of elementary functions, Basic theorems of Laplace transforms, Inverse Laplace transforms, its properties and related theorems, Convolution theorem, Use of Laplace transforms in the solution of differential and integral equations, Evaluation of integrals using Laplace transforms.

Fourier series and transform: Dirichlet conditions, Expansion of periodic functions in Fourier series, Sine and cosine series, The finite Fourier sine and cosine transforms, Complex form of Fourier series, Fourier integral theorem and Fourier transform, Parseval's identity for Fourier series and transforms.

SECTION B

Partial differential equations, One dimensional wave equation, The vibrating string fixed at both ends, D'Alembert and Fourier series solutions, Vibrations of a freely hanging chain, Two dimensional wave equation in rectangular membrane, Wave equation in the two dimensional polar coordinates and vibrations of a circular membrane, 3-D wave equation and its solution, Equation of heat conduction, Two dimensional heat conduction, Temperature distribution in a rectangular and circular plate, 3-D heat conduction equation.

Evaluation of polynomials: Horner's method; Root finding: Fixed point iteration, Bisection method, Regula falsi method, Newton method, Error analysis; System of linear equations: Gauss elimination, Gauss Seidel method, Interpolation and Extrapolation: Lagrange's interpolation, least square fitting;

Differentiation and Integration: Difference operators, Simpson and trapezoidal rules; Ordinary differential equation: Euler method, Taylor method.

Text Books:1. Applied Mathematics: L.A. Pipes and Harwill, Mc Graw Hill Publication2. Mathematical Physics: G.R.Arfken, H.I.Weber, Academic Press, USA (Ind.Ed.)3. Laplace Transforms: M.R. Speigel (Schaum Series), Mc Graw Hill Publication4. Numerical Methods: J.H. Mathews, Prentice Hall of India, New Delhi

Reference Books:1. Advanced Engg. Mathematics: E. Kreyszig, Wiley Eastern Publication

NT 1.1.2 CLASSICAL MECHANICS





Use of scientific calculators is allowed.

Section ALagrangian Formulation: Conservation laws of linear momentum, angular momentum and energy for a single particle and system of particles, Constraints and generalized co-ordinates, Principle of virtual work, D' Alembert's principle and Lagrange's equations of motion, for conservative systems. Applications of Lagrangian formulation.

Variational Principle: Hamilton's principle, Calculus of variations and its application to the shortest distance, minimum surface area of revolution and the brachistochrone problem. Lagrange's equations from Hamilton's principle. Generalized momentum, Cyclic co-ordinates, Symmetry properties and Conservation theorems.

Two body Central Force Problem: Equivalent one body problem, Equations of motion and first integrals, Classification of orbits, Differential equation for the orbit, Kepler problem, Differential and total scattering cross-section, Scattering in an inverse square force field and Rutherford scattering cross section formula, Scattering in lab and center of mass frame.

Section B

Hamiltonian Formulation: Legendre transformation, Hamilton's equations of motion and their physical applications, Hamilton's equations from variational principle, Principle of least action.

Canonical Transformations: Point and canonical transformations, Generating functions, Poisson's brackets and its canonical invariance, Equations of motion in Poisson Bracket formulation, Poisson bracket relations between components of linear and angular momenta. Harmonic oscillator problem, check for transformation to be canonical and determination of generating functions.

Small Oscillations: Eigen value equation, Frequencies of free vibration and normal modes, Normal mode frequencies and eigen vectors of diatomic and linear tri-atomic molecule.

Rigid Body Motion: Orientation of a rigid body, Orthogonal transformations and properties of the orthogonal transformation matrix, Euler angles, Euler's theorem, Infinitesimal rotation, Rate of change of vector in rotating frame, Components of angular velocity along space and body set of axes. Motion of heavy symmetrical top (Analytical treatment).

Text Books:1. Classical Mechanics: H. Goldstein (Narosa Pub.)2. Classical Mechanics: J.C. Upadhyaya (Himalaya Pub. House)

NT 1.1.3 CONDENSED MATTER PHYSICS






SECTION A

Diffraction methods, Lattice vibrations, Free electrons: Diffraction methods, Scattered wave amplitude, Reciprocal lattice, Brillouin zones, Structure factor, Quasi Crystals, Form factor and Debye Waller factor, Lattice vibrations of mono-atomic and diatomic linear lattices, Free electron gas in 1-D and 3-D. Heat capacity of metals, Thermal effective mass, Drude model of electrical conductivity, Wiedman-Franz law, Hall effect, Quantized Hall effect.

Nanotechnology: Introduction to nanoparticles, Metal nano clusters (various types), Properties of semi conducting nanoparticles, Methods of synthesis, Quantum well, Quantum wire and Quantum dots (in brief) and their fabrication. Carbon nanostructures and Energy bands in semiconductors: Carbon molecules, Carbon cluster, C60 (its crystals and superconductivity), Carbon nano tubes, their fabrication and properties, application of carbon nano tubes.

SECTION BOptical processes: Optical reflectance, Kramers-Kronig relations, Electronic inter-band transitions, Excitons and its type, Raman Effect in crystals, Electron spectroscopy with X-rays, Energy loss of fast particles in solids.Semiconductor Physics: Nearly free electron model, Bloch functions, Kronig-penny model, Wave equation of electrons in a periodic potential, Solution of the central equation, Solutions near a zone boundary, Number of Orbitals in a band, Metals and insulators.

Semiconductors and Fermi-surfaces in Metals: Band gap, Equation of motion, properties of holes, Effective mass of electrons (m*), m* in semiconductors, Band structure of Si Ge and GaAs, Intrinsic carrier concentration, Intrinsic and extrinsic conductivity, Thermoelectric Effects, Semimetals, Different zone schemes, Constructions of Fermi surfaces, Experimental methods in Fermi surface studies, Quantization of orbits in a magnetic field, De Haas-Van Alphen effect, Extremal orbits, Fermi surfaces for Cu and Au, Magnetic breakdown.

Text Books:1. Introduction to Solid State Physics; C. Kittel (7th Ed.) , Wiley Eastern, N. Delhi, 19952. Introduction to Nano Technology: Charles P Poole, Jr. and Frank J.Owens, John Wiley & Sons

Publications, 2003

NT 1.1.4 Elective Paper: Option (i) ANALOG ELECTRONICS





Use of scientific calculator is allowed.

SECTION A

Two port network analysis: Active circuit model's equivalent circuit for BJT, Transconductance model: Common emitter. Common base. Common collector amplifiers. Equivalent circuit for FET. Common source amplifier. Source follower circuit (RR1)

Feedback in amplifiers: Stabilization of gain and reduction of non-linear distortion by negative feedback. Effect of feedback on input and output resistance. Voltage and current feedback (RR1)

Bias for transistor amplifier : Fixed bias circuit, Voltage feedback bias. Emitter feedback bias, Voltage divider bias method, Bias for FET (RR1)

Multistage amplifier: Direct coupled CE two stage amplifier. RC coupling and its analysis in mid- high-and low-frequency range. Effect of cascading on bandwidth. Darlington and cascade circuits (RR1)

Oscillators : Feedback and circuit requirements for oscillator, Basic oscillator analysis, Hartley, Colpitts, RC-oscillators and crystal oscillator (RR1)

SECTION-B

Band-pass amplifiers: Parallel resonant circuit and its bandwidth. Tuned primary and tuned secondary amplifiers (RR1)

Power amplifiers: Operating conditions, Power relations, Nonlinear distortion, Class A power amplifier, Push-pull principle, Class B Push pull amplifier (RR1)

Fundamentals of modulation: Frequency spectrum in amplitude modulation, Methods of amplitude modulation, Frequency modulation, Linear demodulation of AM signals, SSB system, AM and FM transmission, Receiving systems (RR1)

Operational amplifiers: Ideal operational amplifier. Inverting and non-inverting amplifiers. Differential amplifiers. CMMR. Internal circuit of operational amplifier. Examples of practical operational amplifier. Operational amplifier characteristics. DC and AC characteristics, slew rate (RR2)

Text Books:1. Electronics Fundamentals and Applications: John D. Ryder (5th Ed.), PHI, New Delhi2. Linear Integrated circuits: D.Roy Choudary and Shail B.Jain, New age international Publishers

NT1.1.4 Elective Paper: Option (ii) REMOTE SENSING


Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examination, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective sections of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carry 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks. Use of scientific calculators is allowed.

SECTION A

History and scope of remote sensing: Milestones in the history of remote sensing, overview of the remote sensing process, A specific example, Key concepts of remote sensing, career preparation and professional development.

Introduction: Definition of remote sensing, Electromagnetic radiation, Electromagnetic Spectrum, interaction with atmosphere, Radiation-Target, Passive vs. Active Sensing, Characteristic of Images.

Sensors: On the Ground, In the Air& in Space, Satellite characteristics, Pixel Size and Scale, Spectral Resolution, Radiometric Resolution, Temporal Resolution, Cameras and Aerial photography, Multispectral Scanning, thermal Imaging, Geometric Distortion, Weather Satellites, Land Observation Satellites, Marine Observation Satellites, Other Sensors, Data Reception.

SECTION B

Microwaves: Introduction, Radar Basics, Viewing Geometry & Spatial Resolution, Image Distortion, Target Interaction, Image Properties, Advanced Applications, Polarimetry, Airborne vs. Spaceborne, Airborne & Spaceborne Systems.

Image Analysis: Visual Interpretation, Digital processing, Preprocessing, Enhancement, Transformations, Classification, Integration.

Applications: Agriculture—Crop Type Mapping and Crop Monitoring; Forestry---Clear cut Mapping, Species identification and Burn Mapping; Geology---Structural Mapping & Geological Units; Hydrology-----Food Delineation & Soil Moisture; Sea Ice----Type & Concentration, Ice Motion; Land Cover----Rural/Urban Change, Biomass Mapping; Mapping-----Planimetry, DEMs, Topo Mapping; Oceans & Coastal-----Ocean features, Ocean Colour, Oil Spill Detection.

Text Books:1. Introduction to Remote Sensing : James B. Cambell2. Fundamentals of Remote Sensing: Natural Resources, Canada Centre of Remote Sensing.

NT 1.1.4 Elective Paper: Option (iii) MICROWAVE AND ITS PROPAGATION






SECTION AMicrowave linear beam tubes: Conventional vacuum tubes, Klystrons, resonant cavities, velocity modulation process, branching process, output power and beam loading; multi cavity klystron amplifiers, reflex klystrons, helix travelling wave tubes, slow wave structures.

Microwave crossed field tubes: Magnetron oscillators: cylindrical, linear and coaxial, forward wave crossed field amplifier, backward wave crossed field amplifier, backward wave crossed field oscillator, their principle of operation and characteristics.

Microwave transistor and tunnel diodes: Microwave bipolar transistors, physical structures, configurations, principles of operation, amplification phenomena, power-frequency limitations, heterojunction bipolar transistors, physical structures, operational mechanism and electronic applications, microwave tunnel diodes, principles of operation, microwave characteristics.

Microwave field effect transistors: Junction field effect transistors, metal semiconductor field effect transistors, high electron mobility transistors, metal oxide semiconductor field effect transistors, physical structures, principle of operation and their characteristics. MOS transistor and memory devices: NMOS, CMOS and memories. Charged coupled devices: Operational mechanism, surface channel CCD's dynamic characteristics.

SECTION B

Transferred electron devices: Gunn effect diodes, Ridley-Walkins-Hilsum theory, modes of operation, LSA diodes, InP diodes, CdTe diodes, microwave generation and amplification.

Avalanche transit time devices: Read diode, IMPATT diodes, TRAPATT diodes, BARITT diodes, their physical structure, principle of operation and characteristics.

Microwave measurements: Measurement of impedance, attenuation, insertion loss, coupling and directivity, frequency, power and wavelength at microwave frequencies.

Microwave transmission lines: Transmission line equations and solutions, reflection coefficient and transmission coefficient, standing wave and standing wave ratio, line impedance and admittance, Smith chart, impedance matching. Microwave cavities, microwave hybrid circuits, directional couplers, circulators and isolators.

Text Books:1. Microwave Devices and Circuits: Sameul Y. Liao, Pearson Education2. Microwaves: K.C. Gupta, Wiley Eastern Limited.

NT 1.1.5 Lab Practice: Electronics

Maximum Marks: 120 Time allowed: 3 HoursPass Marks: 45% Total teaching hours: 125

Out of 120 Marks, internal assessment (based on seminar, viva-voce of experimental reports, number of experiments performed and attendance) carries 30 marks, and the final examination at the end of the semester carries 90 marks.

This laboratory comprises of experiments based on Electronics listed below:

ELECTRONICS EXPERIMENTS: (10 out of the followings)

1. Study the gain frequency response of a given RC coupled BJT, CE amplifier.

2. Study of Clipping & Clamping circuits.

3. Study of shunt capacitor filter, inductor filter, LC filter and filter using Bridge Rectifier.

4. Find the energy gap of a given semi conductor by reverse bias junction method.

5. To calculate the temperature coefficient of Thermistor.

6. Verify De-Morgan’s law and various combinations of gates using Logic gates circuit.

7. Study of various types of Flip-Flops.

8. To study various Oscillators ( Hartley, Colpit, RC Phase shift etc.).

9. To study Amplitude Modulation and De-Modulation and calculate modulation index.

10. To study characteristics of FET and determine its various parameters.

11. Study the characteristics of Tunnel Diode.

12. To study 2 bit, 3 bit and 4 bit Adder & Subtractor.

13. Study the characteristics of basic Thyristors (SCR, MOSFET, UJT, TRIAC etc.).

14. Use of Transistor as a push pull amplifier (Class ‘A’, ‘B’ and ‘AB’).

15. Application of transistor as a series voltage regulator.

16. Study of biasing techniques of BJT.

17. To study Frequency Modulation and Demodulation.

18. Study of transistor as CE, CB and CC amplifier.

19. Fourier series analysis of square, triangular and rectified wave signals.

NT 1.1.6 Computer Laboratory


Out of 60 Marks, internal assessment (based on performance of the candidate in the computer lab and attendance) carries 15 marks, and the final examination at the end of the semester carries 45 marks.

This laboratory comprises of (any ten of the following) physics problems to be solved using computer.

1. To print even and odd numbers between given limit

2. To generate prime numbers between given limit.

3. To construct Fibonacci series.

4. To find maximum and minimum number among a given data.

5. To find area of a triangle.

6. To find factorial of a number.

7. To find roots of a quadratic equation.

8. To construct AP and GP series.

9. To construct Sine and Cosine series.

10. Conversion of temperature scale.

11. Addition of two matrices.

12. Motion of horizontally thrown projectile.

13. Finding mean and standard deviation of a given data.

14. To find perfect numbers.

Semester– II

NT 1.2.1 QUANTUM MECHANICS






SECTION AWave Mechanics: Review of wave mechanical principles. Time independent Schrodinger equation in one, two and three dimensions. Eigen values and Eigen functions. Bound states. Discrete eigen values. Orthogonality of eigen functions. Completeness of eigen functions. Box and function normalization. Expectation values of observables. Uncertainty principle.

Particle in a one dimensional box with finite walls. Two dimensional square with infinite walls. Three dimensional rectangular box with infinite walls and three dimensional square well potential. Isotropic Harmonic oscillator. Degeneracy.

Matrix Mechanics: Postulates of quantum mechanics. Hilbert space. Matrix representation of wave functions and operators. Dirac bra and Ket notations. Change of basis. Harmonic oscillator problem in matrix mechanics creation, destruction and number operators. Orbital angular momentum operators in their polar form . Commutation relation. Matrix representation of orbital angular momentum operators. Eigen values and eigen vectors of L2, Lz spin angular momenta and Pauli spin matrices. Addition of angular momenta. Clebsch-Gordan coefficients. C.G. coefficients of

.

SECTION B

Approximation methods for bound states: Stationary non degenerate perturbation theory, Ist and second order correction to energy levels, Ist order correction to wave functions, Anharmonic oscillator,

Degenerate perturbation theory. Normal Zeeman effect and stark effect of the first excited state of hydrogen.

The Rayleigh Ritz variational method for ground and excited states. Ground state of He atom perturbation and variational approaches and their comparison.

Van der Waal's interaction. Perturbation and vibrational calculations.

One dimensional WKB approximation. Asymptotic behaviour of solutions. Linear turning points. Connection formula and their application to bound state and barrier penetration.

Collision Thoery: Two particle scattering problem. Differential and total scattering cross-section. Lab and CM system of coordinates. Scattering of a particle by a central field. Partial wave analysis. Phase shifts S & P wave scattering. Ramsauer Townsend effect. Resonant scattering. Scattering for a three dimensional square well and rigid sphere. Integral equation for scattering problem. Born approximation. Validity of Born approximation. Screened Coulomb potential.Text Books:1. Quantum Mechanics: L.I. Schiff (Int. Student Ed.), Tata Mc Graw-Hill , New Delhi.2. Quantum Mechanics: J.L. Powell and B. Craseman, Narosa Publishing House, New Delhi.3. Quantum Mechanics; Mathew & Venkatesan, Tata Mc Graw Hill, New Delhi.

NT 1.2.2 DIGITAL ELECTRONICS






SECTION A

Binary, octal and hexadecimal number systems, Inter-conversion of binary to decimal, Decimal to binary, Octal to binary, hexadecimal to binary numbers, Binary arithmetic.

Binary codes, the 8421 code, Gray code and ASCII codes.

Boolean algebra and logic gates-Boolean variables, NOT, AND, OR, NAND, NOR and exclusive OR operation, Boolean identities and laws of Boolean algebra, DeMorgan's theorem, Combinational and sequential logic systems, Minterm and Maxterm and mapping.

Switching properties of semiconductor devices, Diode, BJT and FET as DC and AC switches, Combinational logic circuits using digital ICs.

Sequential and combinational systems. RS, JK, D and T flip-flops, Counters, Synchronous counters, Serial, parallel and mixed counters

SECTION B

Shift registers and ring counters, Universal shift registers

Semiconductors memories, Memory organization and operation, Expanding memory size, Classification and characteristics of memories, Sequential memory, Read only memory, Read and write memory.

Variable register network, Binary ladder, D/A convertor, D/A accuracy and resolution, A/D converters, Simultaneous conversion, Counter method, A/D converters

Characteristics of digital ICs, Classification of logic families, Digital IC packages.

Text Books:1. Digital Principles: A.P. Malvino and D.P. Leach, Tata McGraw-Hill Pub. Co. Ltd. New Delhi.2. Modern Digital Electronics: R.P. Jain, Tata McGraw-Hill Pub. Co. Ltd., New Delhi.

Reference Books:1. Microelectronics: Jacob Millman and Arvin Grabel (3rd Ed.), McGraw Hill Book Co., New Delhi.2. Digital Systems: Principle and Applications: Ronald J. Tocci (Vth Ed.), PHI, New Delhi.3. An Introduction to Digital electronics: M.Singh, Kalyani Publishers, New Delhi.

NT 1.2.3 FUNDAMENTALS TO NANOTECHNOLOGY






SECTION A

Definition of Nanotechnology, Nanoscience & nature, Need of nanotechnology, Size dependence of properties, Quantum confinement effect, Effective mass approximation, Weak confinement regime, Intermediate confinement regime, Strong confinement regime, Empirical pseudopotential method, Tight binding model, Statistical effects of spatial confinement.

Properties of Isolated nanoparticles & nanocrystalline powders: Structural & phase transformations, Crystal lattice constant, Phonon spectrum & heat capacity, magnetic properties, optical properties, catalytic properties.

Effect of grain size & interfaces on the properties of bulk nanomaterials: Mechanical properties, Thermal properties, electric properties, magnetic properties.

Metal Nan clusters: Magic numbers, Theoretical modeling of nanoparticles, Geometric structure, Electronic structure, Reactivity, Fluctuations, Magnetic clusters.

Rare gas & Molecular Clusters: Inert gas clusters, Superfluid clusters, Molecular clusters, Self assembly.Organic compounds and polymers, Biological nanostructures.

Bulk Nanostructure Materials: Solid disordered nanostructures, Nanostructured multi-layers, Metal nanocluster composite glasses, porous silicon.

Nanostructure Crystals: Natural Crystals, Arrays of nanoparticles in zeolites, crystal of metal particles, Nanoparticle lattice in colloidal suspensions, Photonic crystals.

SECTION BCarbon Nanostructures: New carbon structures, Carbon clusters, Carbon nanotubes.

Quantum wells, wires & dots, Semiconductor nanocrystals: Energy levels & density of states in reduced dimension systems, electronic structure & electronic properties, optical properties, catalytic properties, Coulombic explosion, Photofragmentation, Superconductivity & quantum structures.

Nanostructured ferromagnetism: Effect of bulk nanostructuring on magnetic properties, Dynamics of nanomagnets, Nanocarbon ferromagnets, Giant & colossal magneto resistance, Ferrofluids.

Nanomachines & Nanodevices: Microelectromechanical systems(MEMSs), Nanoelectromechanical systems (NEMSs), Molecular mimics; Molecular & supramolecular switches.

Applications of nanomaterials: Quantum dot lasers & light emitting diodes, Photovoltaic solar cells, Optical filters, Phosphors, High density optical data storage devices, Batteries, Smart textile, Nanophotocatalyst, Nanosensors, Insulation materials, Strong & light machine tools, motor vehicles & aircrafts, High power magnets, Medical implants, Drug delivery systems, Nanogenerators, Nanolubricants, Nanopaints.

NT 1.2.3 INTRODUCTION TO NANOTECHNOLOGY

Text Books:

1. Introduction to Nanotechnology by C P Poole Jr. and F J Owens, Published by Wiley Interscience

2. Nanocrystalline Materials by A I Gusev and A A Rempel, Published by Cambridge International Science Publishing.

3. Nanotechnology: Basic Science and Emerging Technologies by M.Wilson,K K G Smith, M Simmons and B Raguse, Published by Chapman & Hall/CRC

4. Springer Handbook of Nanotechnology Edited by Bharat Bhushan, Published by Springer.

NT 1.2.4 Elective Paper: Option (i) APPLIED OPTICS






SECTION A

Fourier Optics: Maxwell's equations and the statement of the diffraction problem in terms of the transmission function. Simple Huygen-Fresnel theory to explain diffraction. Different regions of the diffraction. Fresnel and Fraunhofer approximations. Concept of spatial frequency. Importance of Fourier transformation in optics and its physical interpretation. Physical interpretation of convolution and delta function transform theorems. (RR1)

Use of the Fourier transform to explain Fraunhofer diffraction at a circular aperture. Fraunhofer diffraction at rectangular aperture under various situations. Fresnel diffraction at rectangular aperture and straight edge. Fresnel diffraction and lens. Limitation of geometrical optics. Free space propagation of waves. Phase transmission functions and lens. (RR1)

SECTION B

Polarization: Polarization and double refraction. Explanation of double refraction. Polarization devices: Nicol, Glan, Glan-Thompson, Wollaston, Rochon and Severmont prisms. Wave propagation in anisotropic media. Spatial frequency filtering: The Fourier transforming property of a thin lens. Applications of spatial frequency filtering: Low pass, High pass, Band pass filters. Phase contrast microscope. Image debluring (RR1 & RR2)

Holography: Basic principles, Coherence requirements. Resolution. Gabor holography and distinction with off-axis holography. Fourier transform holograms. Lensless Fourier transform holograms. Computer generated holograms. Volume holograms.

Applications of holography: Microscopy, Interferometry, Character recognition. Holography in optical signal processing. Vander Lugt filter based on Mach-Zender and Rayleigh interferometers. Matched filtering and Fourier transform hologram (RR2)

Text Books:1. Lasers and Optical Engineering: P. Das, Narosa Publishing House, 19922. Optical Electronics: A.K. Ghatak and K. Thyagrajan, Cambridge univ. Press, 1989

NT 1.2.4 Elective Paper: Option (ii) MATHEMATICAL PHYSICS AND CLASSICAL MECHANICS

Maximum Marks: External 60 Time Allowed: 3 Hours Internal 20 Total Teaching hours: 50 Total 80 Pass Marks: 35 %





SECTION A

Cartesian Tensors: Coordinate transformations. Three dimensional rotations. Transformation of vector components under three dimensional rotations. Direct product of two vectors. Tensors of higher rank. Symmetric and antisymmetric tensors. Kronecker and alternating tensors and their isotropy property. Contraction of tensors and differentiation of tensor fields. Expressions for gradient divergence and curl in tensor notation. Vector formulae in tensor notation.

Linear Vector Spaces: Definition, linear independence of vectors, basis and dimensionality. Scalar products of vectors. Orthonormal basis. Gram Schmidt orthogonalization process. Matrix representation of vectors and linear operators. Infinite dimensional vector spaces. Hilbert spaces.

Complex Variables: Complex numbers and variables. Polar form of complex numbers. Functions of complex variables. Cauchy Riemann differential equations. Singularities and their classification. Cauchry integral theorem and formulae. Taylor and Laurent's series, The Cauchy residue theorem and its application to evaluation of real integrals.

SECTION B

Rigid body dynamics: Angular momentum and kinetic energy of rotating rigid body about a fixed point, inertia tensor, Eigen values of inertia tensor, Principal moments and principal axes transformation.

Special Theory of relativity: Lorentz transformation in vector form and orthogonality of Lorentz transformation, Lorentz orthogonal transformation matrix, Equivalent rotation angle and Einstein addition law for parallel velocities, Intervals in four-space and Invariance of Space-time interval, covariant formulation of four space and representation of various vectors in four-space, covariant formulation of Force, momentum and energy equation in Minkowski space, Lagrangian formulation of relativistic mechanics.Relativsitic motion of a particle under a constant force. Relativistic one dimensional harmonic oscillator.

Continuous systems and fields: Transition from discrete to continuous systems. Lagrangian and Hamiltonian formalisms, Stress-energy tensor and conservation laws. Scalar and Dirac fields (only definitions).

Text Books:1. Cartesian Tensors: Harold Jefferies, Combridge University, Press2. Linear Vector Spaces: John Dettman (Hilderbrand)3. Complex Variables: Murrey R. Speigel, Schaum Series, Mc Graw Hill Publication4. Classical Mechanics: H. Goldstein, Narosa Publishing House, New Delhi.

NT 1.2.4 Elective Paper: Option (iii) COMPUTER FUNDAMENTALS AND PROGRAMMING WITH C++






SECTION AComputer organization: Hardware, Memory, Control unit, Arithmetic and logic unit, Input and output devices, software, Programing languages with special reference to C and C++, Assembler, Interpreter and compiler, Application software.

Problem solving with a computer: Problem analysis, Algorithm development, The quality of algorithm, Flowcharts, Program coding, Compilation and execution.

Data types and statements: Identifiers and keywords, Constants, String constants, Numeric constants, Character constants, C++ operators, Arithmetic operators, Assignment operators, Comparison and logic operators, Bitwise logic operators, Special operators, Type conversion.

Writing a programme in C++: Declaration of variables, Statements, Simple C++ programs, Features and iostream.h, Keyword and screen I/O, Manipulation functions, Predefined manipulators, Input and output (I/O) stream flags.

SECTION BControl statements: Conditional expressions, If- statement, If else statement, Switch statement, Loop statements, for- loop, While- loop, do while- loop, Breaking control statements, Break statement, Continue statement and goto statement.

Functions and program structures: Defining a function, Return statement, Types of functions, Actual and formal arguments, Local and global variables, Default arguments, Multifunction program, Storage class specifiers, Automatic variables, Register variables, Static variables, External variables.

Arrays: Array notation, Array declaration and array initialization, Processing with array, Arrays and functions, Multidimensional arrays, Character array.

Pointers: Pointer declaration, Pointer operator, Address operator, Pointer expressions, Pointer arithmetic, Pointer and functions, Call by value, Call by reference.

Structures, unions and bit fields: Declaration of structures, Initialization of structures, Functions of structures, Unions, The union tag, Processing with union, Initialization of unions, Idea of bit fields.

Text Books:1. Programming with C++: D. Ravichandran (2nd Ed.), Tata Mc Graw-Hill Pub. Co. Ltd.2. Object-oriented Programming with C++: R. Balaguruswamy, Tata Mc Graw-Hill Pub. Co. Ltd.

NT 1.2.4 Elective Paper: Option (iv) ATOMIC AND MOLECULAR SPECTROSCOPY






Section A

Hydrogen and Hydrogen-like ions: Series in hydrogen, circular motion, nuclear mass effect, elliptical orbits, energy levels. Fine structure: basic facts and Sommerfeld theory, electron spin and spin-orbit coupling, relativistic correction and Lamb shift (qualitative).

Alkali-like Spectra: General features, doublet structure, Larmor’s theorem and magnetic levels, elementary theory of weak and strong magnetic fields, Zeeman effect in doublet spectra: anomalous Zeeman effect and the anomalous g-value.

Pauli’s principle and shell structure: Systems with several electrons and spin functions.

Complex Spectra: LS-Coupling scheme, normal triplets, basic assumptions of the theory, identification of terms, selection rules, jj- coupling (Qualitative).

Section B

Infrared and Raman Spectra: Rigid rotator, energy levels, spectrum (no derivation of selection rules), Harmonic oscillator: energy levels, eigenfunctions, spectrum, comparison with observed spectrum, Raman effect, Quantum theory of Raman effect, Rotational and Vibrational Raman spectrum. Anharmonic oscillator: energy levels, Infrared and Raman Spectrum, Vibrational frequency and force constants. Non-rigid rotator: energy levels, spectrum, Vibrating-rotator energy levels, Infrared and Raman spectrum (no derivation of Dunham coefficients), Symmetry properties of rotational levels, influence of nuclear spin.

Electronic Spectra: Electronic energy and potential curves, resolution of total energy, Vibrational Structure of Electronic transitions. General formulae, Deslandre’s table, absorption sequences (qualitative) and Vibrational analysis, Rotational Structure of Electronic bands: General relations, branches of a band, band-head formation, Intensity distribution in a vibrational band system. Franck-Condon Principle and its wave mechanical formulation. Classification of electronic states: Orbital angular momentum, Spin, total angular momentum of electrons, Symmetry properties of electronic eigen-functions.

Text Books: 1. Atomic Spectra: H. Kuhn (Longman Green) 1969. 2. Molecular Spectra and Molecular Structure I: G. Herzberg (Van-Nostrand Rein-hold), 1950. 3. Atomic Spectra: H.E. White (McGraw Hill) 1934. 4. Fundamentals of Molecular spectroscopy: Banwell and McCash (Tata McGraw Hill), 1994. 5. Molecular Spectroscopy: S. Chandra (Narosa), 2009. 6. Atomic, Molecular and Photons, Wolfgang Damtrodes (Springer), 2010.

NT 1.2.5 Lab Practice: Laser - Optics


Out of 120 Marks, internal assessment (based on seminar, viva-voce of experimental reports, number of experiments performed and attendance) carries 30 marks, and the final examination at the end of the semester carries 90 marks.

This laboratory comprises of experiments based on Laser & Optics listed below:

LASERS AND OPTICS EXPERIMENTS: (10 out of the followings)

1. To study the optical bench model of microscope and to determine the numerical aperture of the microscope.

2. To study the optical bench model of telescope and to determine the angular field of view and magnifying power by entrance and exit pupil method.

3. To study the characteristics of solar cell.

4. To study the magnetostriction in an iron rod using Michelson interferometer.

5. To study the optical thickness of mica sheet using channel spectrum interferometry.

6. To determine the Planck’s constant using photovoltaic cell.

7. To obtain the coherence matrix and stokes parameters for (i) unpolarized light (ii) polarized light and hence to determine their degree of polarization.

8. To study the aberrations of a convex lens.

9. To study the electro-optic effect in LiNbO3 crystal using He-Ne laser.

10. To study B-H curve.

11. To study the characteristics of optoelectronic devices (LED, Photodiode, Photodiode, Phototransistor, LDR).

12. To study the diffraction pattern by pin hole, single slit, double slit and grating and to calculate the wavelength of He-Ne laser.

13. To study microwave optics system for reflection, refraction, polarization phenomena.

14. To calibrate the prism spectrometer using mercury lamp and to determine the refractive index of material of the prism for a given wavelength of light.

15. Measurement of Brewster angle and refractive index of materials like glass and fused silica (with He-Ne laser) with a specially designed spectrometer.

16. Particle size determination by diode laser

17. Study of optical fiber communication kit.

NT 1.2.6 Computer Laboratory


Out of 60 Marks, internal assessment (based on performance of the candidate in the computer lab and attendance) carries 15 marks, and the final examination at the end of the semester carries 45 marks.

This laboratory comprises of any ten of the following physics problems to be solved using computer.

1. To generate Frequency Distribution Table.

2. Solution of a differential equation by RK2 method.

3. To find area under a curve by Trapezoidal Rule and Simpson’s Rule

4. Gauss elimination method.

5. Multiplication of Two Matrices.

6. Motion of Projectile thrown at an Angle.

7. Numerical Solution of Equation of Motion.

8. Simulation of planetary motion.

9. Root of an equation by Newton- Raphson method.

10. Sorting numbers by selection sort.

11. Solution of a differential equation by RK4 method.

12. Fitting straight line through given data points.

13. Roots of an equation by secant method.

14. Newton interpolation.

For Other Departments Students: Qualifying Paper

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