DWARAKA DOSS GOVERDHAN DOSS VAISHNAV …dgvcphysics.yolasite.com/resources/I M.Sc. Physics...

DWARAKA DOSS GOVERDHAN DOSS

VAISHNAV COLLEGE

(Linguistic Minority Institution)

[AUTONOMOUS] Accredited at „A‟ grade by NAAC

(effective from 2011-12)

“Gokulbagh” 833, Periyar E.V.R. Salai,

Arumbakkam, Chennai – 600106. Ph: 2475 4349

E-mail: [email protected]

2

ANNEXURE - I

A general overview of the four-semester programme, including the

courses, hours and the credits [Effective from the academic year 2011-2012]

SEMESTER I

S. No Course

component Name of course Inst.

hours credits Max. marks

CIA external Total

1 core Paper1– Mathematical

Physics - I 6 hours 5 25 75 100

2 core Paper 2 – Classical

Mechanics and Relativity 5 hours 5 25 75 100

3 core Paper 3 – Quantum

Mechanics-I 6 hours 5 25 75 100

4 core Paper 4 – Integrated

electronics and

Microprocessor 8085

5 hours 5 25 75 100

5 core Paper 5 – Practical I 3 hours Practical examination at the end of

Semester II 6 core Paper 6 -- Practical II 3 hours

7 Soft Skill I 2 hours 2 40 60 100

TOTAL 30 22 140 360 500

SEMESTER II

S. No Course



CIA external Total 8 core Paper 7– Mathematical

Physics - II 6 hours 5 25 75 100

9 core Paper 8 – Quantum

Mechanics-II

6 hours 5 25 75 100

10 core Paper 5– Practical I 3 hours 5 25 75 100

11 core Paper 6– Practical II 3 hours 5 25 75 100

12 Elective –I* Paper 9 5 hours 5 25 75 100

13 EDP- I** Paper 10 5 hours 5 25 75 100


TOTAL 30 32 190 510 700

3

SEMESTER III

S. No Course



CIA external Total 15 core Paper11– Statistical

Mechanics 6 hours 5 25 75 100

16 core Paper12–

Electromagnetic theory &

Plasma Physics

5 hours 5 25 75 100

17 core Paper 13– Practical - III 3 hours Practical examination at the end of

Semester IV 18 core Paper 14 - Practical - IV 3 hours

19 Elective II Paper 15 4 hours 4 25 75 100 20 EDP - II** Paper 16 4 hours 4 25 75 100 21 Soft Skill I 2 hours 2 40 60 100

TOTAL 27 20 140 360 500

SEMESTER IV

S. No Course

component Name of course Inst. hours credits Max. marks

CIA external Total 22 core Paper17 – Condensed

Matter Physics 6 hours

5 25 75 100

23 core Paper18 – Nuclear &

Particle physics 6 hours

5 25 75 100

24 Core Paper 12 -- Practical - III 3 hours 5 25 75 100 25 Core Paper 13-- Practical - IV 3 hours 5 25 75 100 27 Core Paper 20 – Project 2 hours 4 25 75 100 24 Elective III Paper 19 – Computational

methods and C programming

5 hours 5 25 75 100


TOTAL 27 31 190 510 700

4

*ELECTIVE PAPERS

Elective I – Paper 9

Any one of the following: 1. Spectroscopy

2. Digital communication

Elective II and III – Papers 15 and 20

Any two of the following: 1. Microprocessor and microcontroller

2. Computational methods and C programming

3. Advanced spectroscopy

**Extra Disciplinary Electives – Papers 10 and 16

Any two of the following: 1. Recent trends in Physics

2. Hyperfine techniques and Surface Spectroscopies

3. Basic quantum mechanics

4. Basic material science

5. Mathematical methods

6. Classical Dynamics

7. Crystal Growth Techniques

8. Intelligent instrumentation

Practicals

Practical I: General Physics experiments

Practical II: Electronics

Practical III: Microprocessor 8085 & Microcontroller 8051

Practical IV: Microprocessor 8086 & Computational methods and programming

5

ANNEXURE - II

Question paper pattern (Theory courses)

[Effective from the academic year 2011-2012]

Duration: 3 hours Max. Marks: 75

Part – A

10 questions x 2 mark each = 20 marks

(10 out of 12, atleast 2 questions from each unit)

Part – B

5 questions x 5 marks each = 25 marks

(5 out of 7 questions, covering all 5 units)

Part – C

3 questions x 10 marks each = 30 marks

(3 out of 5 questions, covering all 5 units)

NOTE : Students are advised to check the credit awarding pattern with the Department.

Rules and regulations may change time to time.

6

ANNEXURE - III

Marks distribution pattern [Effective from the academic year 2011-2012]

Theory papers

Internal assessment: 2 tests out of 3 : 15 marks

Attendance : 5 marks

Assignment/seminar : 5 marks

TOTAL : 25 marks

External marks: 75 marks

Total (internal + external) = 100 marks

Practical papers



Record : 5 marks

TOTAL : 40 marks

External marks : 60 marks

Practical : Record: 10 marks; Experiment: 50marks

Total (internal + external) = 100 marks

Project

Internal assessment: 2 out of 3 presentations : 25 marks

External marks: Viva : 25 marks

Project report : 50 marks

TOTAL : 100 marks

7

DWARAKA DOSS GOVERDHAN DOSS VAISHNAV COLLEGE

(Linguistic Minority Institution) [AUTONOMOUS]

Accredited at „A‟ grade by NAAC

DEPARTMENT OF PHYSICS

M.Sc DEGREE COURSE IN PHYSICS

Syllabus

Semester I

Paper1. Mathematical physics I No. of credits: 5

No. of hours allotted:6/ Week

Unit I: Vector Analysis

Scalar field, vector field, gradient, divergence, curl, Laplacian, - Expression for gradient,

divergence, curl, Laplacian in orthogonal curvilinear coordinates, spherical coordinates

and cylindrical coordinates- Line, Surface and Volume integrals of vectors- problems

and applications - Stoke’s theorem - Green’s Theorem – Green’s theorem in a plane-

Vector integration - Application of vectors: equation of continuity, Euler’s equation of

motion, Bernoulli’s theorem, Toricelli theorem

Unit II: Linear differential equations and special functions

Second order linear differential equations – solution by power series method (Forbenius

method)

Legendre, Laguerre and Hermite differential equations – expansion of polynomials -

Bessel’s functions- Beta functions - gamma functions – their applications

Unit III: Dirac delta, Green‟s fuction and Vector space

Dirac-delta function- Dirac delta calculus- applications

One-dimensional Green’s function – Eigen function expansion of the Green’s function –

Reciprocity theorem – Sturm-Liouville type equations in one dimension and their

Green’s functions

Vectors in n-dimensions – matrix representations of vectors and operators in a basis –

linear independence, dimension – inner product – Schwartz inequality – orthonormal

basis – Gram-Schmidt process – Eigen values and Eigen functions of operators

8

Unit IV: Matrices

Basic concepts of matrix algebra- Types of matrices and their properties: square matrix,

null matrix, row and column matrix, triangular matrix, diagonal matrix, scalar matrix,

unit matrix, periodic matrix, symmetric and anti-symmetric matrix, skew symmetric

matrix, Hermitian matrix, skew Hermitian matrix, Unitary and orthogonal matrix –

Conjugate of a matrix- Adjoint of a matrix - Inverse of a matrix- Trace of a matrix -

transformation of matrices- Charecteristic equation- Eigen values and Eigen vectors- their

nature- Cayley Hamilton theorem- Diagonalisation of matrix- Application of matrices:

Solution of Linear equations using matrices- Cramer’s rule

Unit V: Group theory

Group axioms- definition : subgroup, simple group, Abelian group, cyclic group, order of

a group, class, isomorphism, homomorphism - Lagrange’s theorem statement and proof-

Symmetry operations and respective symmetry elements: Identity, rotation, reflection,

rotation reflection, inversion - symmetry operations of a rectangle, equilateral triangle -

application : construction of group multiplication table ( not character table) for groups of

order 2, 3,cyclic group of order 4, noncyclic group of order 4, D3 group- definition of a

point group - symmetry operations of water – symmetry operations of ammonia- Great

Orthogonality theorem (only statement, no proof, no derivation)- rules to form a character

table - application : construction of character table for C2v (water) and C3v (ammonia)

Books for study:

1. Mathematical Physics - Sathyaprakash, Sultan Chand & Co

2. Mathematical Physics - B.S.Rajput, PragathiPrakasan, 2007

3. Mathematical Physics - B.D. Gupta , Vikas publishing house reprint 1999

4. Group theory and symmetry in Chemistry, Gurdeep Raj, Ajay Bhagi, Vinod Jain,

Krishna Prakashan Media Publishers, Meerut

5. Mathematical Physics - P.K. Chattopadhyay ,Wiley Eastern, Chennai, 1990

6. Matrices and tensors for physics, 3rd

edition – A.W. Joshi (Wiley Easter, Chennai,

1995)

7. Elements of group theory for Physicists, Wiley Eastern Ltd.

Books for reference:



1995)

2. Mathematical Physics - E. Butkov, Addison-Wesley, Reading, Massachusetts,

1968

3. Mathematical Methods for Physicists – Arfken, Weber, 6th Edition, Elsevier

Publication

9

4. Mathematical Methods – Potter, Goldberg, 2nd

Editionl Prentice-Hall, India

5. Mathematical Methods for Physics and Engineering – Riley, Hobson, Bence, 2nd

Edition, Cambridge Low-price edition

6. Special Functions – M.D. Raisinghania, (published by Kedarnath and Ramnath,

4th revised edition)

7. Advanced Engineering Mathematics – E. Kreyszig, 8th Edition, Wiley, New York



10

Paper 2. Classical mechanics and relativity [Effective from the academic year 2011-2012]

No. of credits: 5

No. of hours allotted: 5/ Week

Unit I: Lagrangian and Hamiltonian Formulations

Generalized coordinates - Principal of virtual work - D’ Alembert’s principle –

Lagrange’s equations from D’ Alembert’s principle – Lagrange’s equations from

Hamilton’s variational principle - Generalized momentum - Cyclic coordinates -

Hamiltonian - Hamilton’s canonical equation of motion – Applications - Scattering by

central potential – Kepler’s law.

Unit II: Mechanics of rigid bodies

Rigid body motion – kinematics- Euler’s angles - infinitesimal rotations – rate of change

of a vector – Coriolis force – Expression for Coriolis force- dynamics –Angular

momentum and kinetic energy – moment of inertia tensor – Euler’s equations of motion –

torque-free motion – symmetrical top - Effective potential of symmetric top -

Introduction to types of motion of top - Steady precession, Nutation, Fast top(no

mathematical derivation).

Unit III: Canonical transformation

Canonical transformations and their generators – Simple examples – Poisson brackets –

equations of motion in Poisson bracket formalism –Symmetries and conservation laws –

Hamilton - Jacobi theorem – Application to harmonic oscillator problem

Unit IV: Small oscillations

Stable, unstable, neutral equilibrium - Potential energy curve - One dimensional oscillator

- Two coupled oscillator – solution - normal co-ordinates – frequencies of normal modes

-kinetic and potential energy in normal co-ordinates - General theory of small oscillations

- secular equation - Eigen values - Solution – Application - Linear tri atomic molecule.

Unit V: Relativity

Minkowski space - Lorentz transformation – Four-vectors – Examples of four vectors -

position, velocity, momentum, acceleration - Lorentz invariance of the four product of

two four vectors – Invariance of Maxwell’s equations – Relativistic Lagrangian and

Hamiltonian for a free particle.

11

Books for study:

1. Classical Mechanics – H. Goldstein, 3rd

edition, Pearson Education Asia, New

Delhi, 2002.

2. Classical Mechanics – C.R. Mondal, Prentice – Hall of India, New Delhi.

3. Classical Mechanics – Gupta and Kumar.

4. Classical Mechanics – J.C.Upadhyaya, Himalaya Publishing Co., New Delhi,

1999


1. Classical Mechanics – Rana and Joag, Tata McGraw Hill, 2003

2. Mechanics – L.D. Landau and E.M. Lifshitz, Pergomon Press, Oxford, 1969

3. Principles of classical mechanics – J.L. Synge and B.A. Griffith, Mc Graw-Hill,

New York, 1949

12

Paper 3. Quantum Mechanics I [Effective from the academic year 2011-2012]

No. of credits: 5

No. of hours allotted:6 / Week

Unit I: Basic formalism

Interpretation and conditions on the wave functions – Postulates of quantum mechanics -

Schrodinger equation – Ehrenfest’s theorem – stationary states – Hermitian operators for

dynamical variables – Eigen values - Eigen functions – uncertainty principle.

Unit II: One dimensional problems and three dimensional problems

Particle in a box - Square-well potential – Barrier penetration – simple harmonic

oscillator – ladder operators method.

Orbital angular momentum - spherical harmonics – Central forces - reduction of two

body problem – Particle in a spherical well – Hydogen atom.

Unit III: General formalism

Hilbert space – Dirac notation – coordinate representation - momentum representations –

time evolution – Schrodinger, Heisenberg and interaction pictures – symmetries and

conservation laws – Unitary transformations associated with translations-Unitary

transformations associated with rotations – parity - time reversal.

Unit IV: Approximation methods

Time-independent perturbation theory for non-degenerate level - Time-independent

perturbation theory for degenerate levels – Stark effect - variation method - ground state

energy of helium atom- JWKB approximation –Application to simple harmonic oscillator

– connection formula ( no derivation ).

Unit V: Angular momentum and identical particles

Eigen value spectrum from angular momentum algebra – matrix representation – spin

angular momentum – addition of angular momenta – Clebsch-Gordan coefficients

Identical particles - Symmetry and anti-symmetry of wave functions – spin and statistics-

Pauli matrices.

13

Books for study:

1. A Text book of Quantum Mechanics – P.M. Mathews and K. Venkatesan (Tata

McGraw-Hill, New Delhi, 1976)

2. Quantum Mechanics - G. Aruldhas (Prentice Hall of India, New Delhi, 2002).

3. Quantum Mechanics: Theory and applications, 4th

edition – A. Ghatak and S.

Lokanathan ( Macmillar India)

4. Quantum mechanics – L.I. Schiff (McGraw Hill, International student edition,

3rd

Ed., 1968)

5. Quantum mechanics – V.Devanathan ( Narosa Publishing House, New Delhi,

2005)


1. Quantum Mechanics – E. Merzbacher, 2nd

Edition, John Wiley and Sons, New

York, 1970.

2. The Feynman Lectures on Physics – R. P. Feynman, R.B. Leighton and M.

Sands, Vol. 3, Narosa Publication, New Delhi

3. Introduction to Quantum Mechanics – Griffiths, 2nd

Edition,

14

Paper 4: Integrated Electronics and Microprocessor 8085 [Effective from the academic year 2011-2012]

No. of credits: 5


Unit I: Semiconductor devices

FET, MOSFET, UJT, SCR, TRIAC – constructional features – working principle and

I-V characteristics – FET as Common Source and Common Drain amplifier – Biasing

of FET and MOSFET – UJT relaxation oscillator – SCR, TRIAC for power control.

IC Technology – Monolithic, Thin film and Hybrid technologies – Limitations in IC

technology – VLSI.

Unit II: Digital Electronics

Sequential logic circuits – 1-bit memory, Latch, R-S Flip flop, J-K Flip flop – Race-

around comdition – master – Slave Flip flop – T and D flip flops.

Registers, Modes of operation, shift right, shift left registers. Counters (4 bit). Ripple

(or) asynchronous Counters – synchronous counters –Up - down counters – decade

counter – BCD counter.

Timer 555 – internal architecture and working – Monostable and Astable operation.

Voltage control oscillator (VCO) IC 566 – PLL concept

Unit III: Applications of Op-Amps

D/A convertor - Binary Weighted resistor - R-2R ladder, A/D convertor - flash type -

counter type- successive approximation - dual slope.

Active filter circuits – Low pass, High Pass, Band Pass- 1st order, 2

nd Order

Butterworth filter circuits – Wide Band and Narrow band reject Filters.

DC Analysis of IC Op-Amp - Instrumentation amplifier - Transducer Bridge

Instrumentation Amplifier- Applications-Temperature indicator - Analog Integrator,

differentiator - Design of analog circuits for solution of differential equation using Op

amps -simultaneous equations using Op amp - Sample and Hold circuit.

Unit IV: 8085 Programming and Interfacing

Architecture-Pin Configuration-Addressing modes – instruction set – Programming

techniques-Addition, Subtraction, Multiplication, Division of 8 bit numbers, Square

15

and Square root of a 8 bit number, Hex to BCD, BCD to Hex – Assembly language

programs.

Interfacing Memory and I/O – Memory system –– Two dimensional addressing- 2K

X 8, 4K X 8 ROM Interface – 2K X 8,4K X 8 RAM Interface – Timing diagram for

Memory READ and Memory WRITE cycles.

Unit V: Port Interfacing

8255-IN and OUT Instructions – timing diagram – Device selection – Design of Input

port and Output port using I/O – Mapped I/O techniques – Difference between I/O

mapped I/O, memory mapped I/O – simple Polled I/O and Hand shaking operations.

Books for study:

1. Semiconductor Devices – Physics and Technology, S.M. Sze, 1985, Wiley, New

york.

2. Integrated Electronics - Millman and Halkias, Tata McGraw Hill

3. Electronic Devices and Circuits - Millman and Halkias, Tata McGraw Hill

4. OPAmps and integrated circuits - R.A Gaekwad, 1994, EEE.

5. Digital Integrated Electronics - Taub and Shilling, 1983, McGraw-Hill, New

Delhi

6. Digital Electronics - Malvino and Leech, fifth edition, Tata McGraw Hill

7. Digital and Analog Circuits and Systems, J.Millman, 1979, McGraw-Hill,

London.

8. Microprocessor Architecture, Programming and application with the 8085, R.S.

Gaonkar, 1997, 3rd

Edition, Penram International Publishing, Mumbai.

9. Fundamentals of microprocessor-Architecture, Programming and Interfacing – V.

Vijayendran, Viswanathan Printers, Chennai

Books for reference

1. Principles of Electronics – V.K. Mehta , S.Chand&co.ltd.,1999

2. Electronic Devices and Circuit Theory – R.L. Boylestad and L. Nashelsky, 8th

Edition, Pearson Education

3. Fundamentals of Microprocessors and Micro computers – B. Ram, Dhanpat Rai

Publications, New Delhi

4. Introduction to Semiconductor Devices – M.S. Tyagi, Wiley, New York,2004

16

Paper 5 Practical I [Effective from the academic year 2011-2012]

General



Record : 5 marks

TOTAL : 40 marks

External marks (TOTAL: 60 marks)


Any 14 experiments

1. Cornu’s method – Young’s modulus by elliptical fringes

2. Young’s modulus – Hyperbolic fringes.

3. Stefan’s constant

4. Band gap energy – Thermistor/semiconductor(using Post Office box)

5. Hydrogen spectrum – Rydberg constant

6. Lasers – study of laser beam parameters

7. Arc spectrum – copper

8. Viscosity of liquid – Meyer’s disc.

9. F. P. Etalon using spectrometer.

10. Arc spectrum – Iron.

11. Specific charge of an electron – Thomson’s method. 12. B-H curve using CRO

13. GM counter – Characteristics, inverse square law, absorption coefficient.

14. GM counter - Feather’s analysis : Range of Beta rays.

15. Hall effect.

16. Susceptibility by Quincke’s method.

17. Susceptibility by Guoy’s method. 18. Ultrasonics – Compressibility of a liquid


1. D. Chattopadhyay, P.C Rakshit, and B. Saha, 2002, An Advanced Course in Practical

Physics, 6th Edition, Books and Allied, Kolkata.

17

Paper 6 : Practical - II [Effective from the academic year 2011-2012]

Electronics



Record : 5 marks

TOTAL : 40 marks

External marks (TOTAL: 60 marks)


Any TWELVE Experiments:

1. Study of attenuation characteristics of Wien bridge network and Wien bridge

oscillator using OP AMP.

2. Study of attenuation characteristics of phase shift network and phase shift

oscillator using OP AMP.

3. Op amp - Schmitt trigger.

4. Op amp – astable and monostable multivibrators

5. Study of R-S, clocked R-S, D flip-flops using NAND gates.

6. Study of J-K, D and T flip-flops using IC 7473.

7. Clock generators using IC 7400 and 7413 using microprocessor 8085.

8. Op.amp. – solving simultaneous equations

9. Op.amp. – 4-bit D/A converters using R-2R ladder network

10. Op.amp. – 4-bit D/A converters using R-2R ladder network

11. Op.amp. – active filters

12. IC 555 timer – Astable Multivibrator and VCO

13. IC 555 timer – Schmitt trigger

14. IC 7473/76 – shift register, ring counter & Johnson counter

15. Arithmetic operations using IC 7483 and IC 7486

16. IC 7490 as scalar and seven segment display using IC 7447

Book for Reference:

1. D. Chattopadhyay, P. C. Rakshit, and B. Saha, 2002, An Advanced Course in

Practical Physics, 6th Edition, Books and Allied, Kolkata.

18

Semester II

Paper 7. Mathematical Physics II [Effective from the academic year 2011-2012]

No. of credits: 5


Unit I: Complex variables

Complex numbers- complex algebra- analytic functions- Cauchy Riemann conditions-

singular points- Cauchy’s theorem- Cauchy integral formula- Taylor’s series- Liouville’s

theorem from Taylor’s series- Laurent’s series-zeroes and singularities- residue and

poles- residue theorem and its applications-evaluation of definite integrals

Unit II: Fourier series and integrals

Basic definitions- evaluation of evaluation of coefficients of Fourier series- problems-

advantages of Fourier series- Parseval’s theorem- Application of Fourier series : analysis

of periodic waveforms, full wave rectifier- Fourier integrals

Unit III: Integral transforms

Laplace transform- linearity, shifting, change of scale properties- derivative of Laplace

transform-integration of Laplace transform -inverse Laplace transform- properties-

problems

Fourier transform- Fourier integral-introduction to Fourier Sine transform-Fourier cosine

transform- simple applications

Unit IV: Tensor analysis

Definition of tensors in three dimensions : scalars, vectors- tensors in Minkowski world-

rank of a tensor- covariant, contravariant and mixed tensors-symmetric and

antisymmetric tensors- Fundamental rules of tensor analysis : addition, subtraction, direct

product, quotient rule- index notation and summation conventions- invariant tensor-

Christoffel’s symbols of I and II kind- properties- transformation laws- application of

tensor analysis to dynamics of a particle( Lagrange’s equation)

Unit V: Probability, theory of errors and curve fitting

Probability- dependent and independent events- mutually exclusive events- repeated and

independent trials- binomial law of probability-multinomial law-sample space and

events- random variables-Binomial, Poisson, normal(Guassian) distributions- standard

deviations- meam-mode-variance-principle of least squares-curve fitting

19

Books for study:

8. Mathematical Physics - Sathyaprakash, Sultan Chand & Co

9. Mathematical Physics - B.S.Rajput, PragathiPrakasan, 2007

10. Mathematical Physics - B.D. Gupta , Vikas publishing house reprint 1999

11. Group theory and symmetry in Chemistry, Gurdeep Raj, Ajay Bhagi, Vinod Jain,

Krishna Prakashan Media Publishers, Meerut

12. Mathematical Physics - P.K. Chattopadhyay ,Wiley Eastern, Chennai, 1990



1995)

14. Elements of group theory for Physicists, Wiley Eastern Ltd.




1995)

10. Mathematical Physics - E. Butkov, Addison-Wesley, Reading, Massachusetts,

1968

11. Mathematical Methods for Physicists – Arfken, Weber, 6th Edition, Elsevier

Publication

12. Mathematical Methods – Potter, Goldberg, 2nd

Editionl Prentice-Hall, India

13. Mathematical Methods for Physics and Engineering – Riley, Hobson, Bence, 2nd

Edition, Cambridge Low-price edition



15. Advanced Engineering Mathematics – E. Kreyszig, 8th Edition, Wiley, New York

20

Paper 8: Quantum Mechanics II


No. of credits: 5


Unit 1: Scattering Theory

Scattering amplitude – Differential scattering cross section- Relation between scattering

amplitude and scattering cross section -First Born approximation – Expression for

scattering amplitude - Partial wave analysis – Optical theorem - Effective range theory

for S-wave.

Unit 2: Perturbation Theory

Time dependent perturbation theory – Fermi golden rule - harmonic perturbation -

Transition probabilities – Emission and absorption of radiation- Einstein’s co-efficients

of spontaneous emission , stimulated emission - Adiabatic approximation - Sudden

approximation .

Unit 3: Relativistic Quantum Mechanics

Klein-Gordon equation –Probability and current densities - Drawbacks of K-G equation -

Dirac equation –Properties of α and β matrices - Plane-wave solution of Dirac equation -

Interpretation of negative energy states - Probability and current densities.

Unit 4: Dirac Equation

Covariant form of Dirac equation - Properties of the gamma Matrices - Traces -

Relativistic invariance of Dirac equation – Probability density - current four vector –

Bilinear covariants - Feynman's theory of positron (Elementary ideas only without

propagation formalism).

Unit 5: Second Quantization

Field function –– Quantization procedure for particles – Lagrangian density – Euler-

Lagrange equation for classical field – Hamiltonian density – Second Quantization of real

scalar field (Klein-Gordon field) – Creation, annihilation and number operators -

Commutation relations.

21

Books for Study:

1. P. M. Mathews and K. Venkatesan, 1976, A Text book of Quantum Mechanics,

Tata McGraw-Hill, New Delhi.

2. L. I. Schiff, 1968, Quantum Mechanics, 3rd

Edition, International Student Edition,

MacGraw-Hill Kogakusha, Tokyo.

3. Gupta, Kumar and Sharma, 2005, Quantum Mechanics, Jai Prakash Nath&Co.

Meerut.

4. V. K. Thankappan, 1985, Quantum Mechanics, 2nd

Edition, Wiley Eastern Ltd, New

Delhi.

5. J.D. Bjorken and S.D. Drell, 1964, Relativistic Quantum Mechanics, MacGraw-Hill

New York.

6. V. Devanathan, 2005, Quantum Mechanics, Narosa Publishing House, New Delhi.

Books for Reference:

1. P. A. M. Dirac, 1973, The Principles of Quantum Mechanics, Oxford University

Press, London.

2. L. D. Landau and E. M. Lifshitz, 1958 Quantum Mechanics, Pergomon Press,

London.

3. S. N. Biswas, 1999, Quantum Mechanics, Books and Allied, Kolkata.

4. G. Aruldhas, 2002, Quantum Mechanics, Prentice-Hall of India, New Delhi.

5. J. S. Bell, Gottfried and M.Veltman, 2001, The Foundations of Quantum

Mechanics, World Scientific.

6. V. Devanathan, 1999, Angular Momentum Techniques in Quantum Mechanics,

Kluwer Academic Publishers, Dordrecht.

Paper 9: ELECTIVE I

Paper 10: EDP I

22

Electives

(SPECTROSCOPY OR DIGITAL COMMUNICATION)


Spectroscopy

No. of credits: 5


Unit 1: Microwave Spectroscopy

Rotational spectra of diatomic molecules – reduced mass - rotational constant - effect of

isotopic substation – non rigid rotator – centrifugal distortion constant - Polyatomic

molecules - Linear - symmetric top molecules - Hyperfine structrure and quadrupole

moment of linear molecules – Instrumentation techniques – block diagram - Stark effect.

Unit 2: Normal Coordinate Analysis

Raman and IR activity C2V and C3V point groups –- NCA of water - Internal

coordinates of water- Normal modes of vibration of water- - IR and Raman activity of

normal modes- Character table for water - Molecular Vibrations in terms of symmetry

coordinates- Orthonormalisation of symmetry coordinates- Orthonormal symmetry

coordinates.

Unit 3: Infrared Spectroscopy

Vibrations of simple harmonic oscillator – zero point energy - Anharmonic oscillator –

fundamentals and overtones – diatomic vibrating rotator – PR branch - PQR branch –-

fundamental modes of Vibration of water - carbon di oxide - Introduction to application

of Vibrational Spectra – Instrumentation techniques – FTIR spectroscopy

Unit 4: Raman Spectroscopy

Classical theory – molecular polarizability – polarizability ellipsoid – quantum theory of

Raman effect - Rotational Raman spectra of linear molecule – symmetric top molecule-

Stokes and antistokes line – SR branch - Raman activity of water – carbon di oxide -

Mutual Exclusion principle – determination of N2O structure- Instrumentation technique

and block diagram – Structure Determination of planar and AB3 molecule, SO2 through

IR and Raman spectroscopy

23

Unit 5: UV Spectroscopy

Origin of UV spectra – laws of absorption – Lambert Bouguer law- Lambert Beer law –

molar absorptivity – Transmittance and absorbance – instrumentation – Single beam UV

spectrophotometer – Double beam UV spectrophotometer – Simple applications

Books for Study:

1. C. N. Banwell and E. M. McCash, 1994, Fundamentals of Molecular Spectroscopy,

4th Edition TMH, New Delhi.

2. G. Aruldas, , Moleclar Structure and Spectroscopy, Prentice Hall of India Pvt. Ltd.

New Delhi. 2001

3. D. N. Satyanarayana, Vibrational Spectroscopy and Applications, New Age

International Publication, 2004,

4. B.K.Sharma, Spectroscopy, Goel Publishing House Meerut, 2005.


1. D. D. Jyaji and M. D Yadav 1991, Spectroscopy, Amol Publications

2. Atta ur Rahman, 1986, Nuclear Magnetic Resonance, Spinger Verlag.

3. D. A. Lang, Raman Spectroscopy, Mc Graw-Hill International

4. Raymond Chang, 1980, Basic Principles of Spectroscopy Mc Graw-Hill Kogakusha,

Tokyo.

24

Digital Communication


No. of credits: 5


Unit 1: Signal Analysis

Fourier transforms of gate functions, delta functions at the origin – Two delta function

and periodic delta function – Properties of Fourier transform – Frequency shifting –Time

shifting - Convolution –Graphical representation – Convolution theorem – Time

Convolution theorem –Frequency Convolution theorem –Sampling theorem.

Unit 2: Information Theory

Communication system – Measurement of information – Coding – Bandot Code-CCITT

Code –Hartley Law – Noise in a information Carrying Channel- Effects of noise-

Capacity of noise in a channel – Shannon Hartley theorem –Redundancy.

Unit 3: Pulse Modulation

Pulse amplitude modulation - natural sampling – Instantaneous sampling - Transmission

of PAM Signals -Pulse width modulation – Time division multiplexing – Band width

requirements for PAM Signals. Pulse Code Modulation –Principles of PCM –Quantizing

noise – Generation and demodulation of PCM -Effects of noise –Companding –

Advantages and applications of PCM – Other digital pulse modulating systems

Differential PCM –Delta modulation.

Unit 4: Error Control Coding

Introduction to Linear Block Codes, Hamming Codes, BCH Coding, RS Coding,

Convolutional Coding, Coding Grain Viterbi Coding.

Unit 5: Spread Spectrum Systems

Psuedo Noise sequences, generation and Correlation properties, direct sequence spread

spectrum systems, frequency HOP Systems, processing gain, antijam and multipath

performance.

Books for Study

1. B.P. Lathi, Communication system, Wiley Eastern.

2. George Kennedy, Electronic Communication Systems, 3rd

Edition, McGraw Hill.

25

3. Simon Haykin, Communication System, 3rd

Edition, John Wiley & Sons.


1. Simon Haykin, 1988, Digital Communication, John Wiley,.

2. John Proakis, 1995, Digital Communication, 3rd

Edition, McGraw Hill, Malaysia.

3. M. K. Simen, 1999, Digital Communication Techniques, Signal Design and

Detection, Prentice Hall of India.

26

EXTRA DISCIPLINARY PAPER

(Any one of the following papers)

Recent Trends in Physics [Effective from the academic year 2011-2012]

No. of credits: 4


Unit I: Fundamentals of Crystal Growth

Classification of materials – Structure Property relationship in materials – The

statistical nature of entropy – the space lattices – Bravias Lattices - Crystal Structure -

Miller indices – Crystal directions and planes.

Unit II: Phase Diagram and Nucleation Kinetics

The Phase rule – single component system – binary phase diagram – microstructural

change during cooling – Lever rule - Time scale for phase changes – Nucleation kinetics

– the growth and overall transformation kinetics.

Unit III: Introduction to Crystal growth techniques

Solution growth – saturation and super saturation – solubility curve – metastable zone

with – growth by evaporation of solvent method – slow cooling method – temperature

gradient method (overview) – growth from flux - growth by evaporation of solvent

method – slow cooling method – temperature gradient method (overview) – growth from

melt – Czochralski method – zone refining – skull melting process.

Unit IV: Characterisation of materials ( only instrumentation technique and

overview)

Structure determination – XRD – TGA – DTA – TEM – SEM.

Unit V: Introduction to Nano Science and Nano Techonology

Introduction to Nano science and techonology – importance – classification – properties –

electrical – maganetic – optical materials – basic physics of nano materials – quantum

confinement – quantum dots – smart materials – Moore’s law and nano circuitory – nano

wire – nano crystals – bio sensors.

Books for study:

27

1. Ragavan .V., Materials science and Engineering – a first course PHI New Delhi

(fifth Edition).

2. S. Shanmugam Nanotechnology,M.J.Publications (2003)

3. C.N. Banwel and E.M. McCash, Fundamentals of Molecular Spectroscopy, 4th

Ed. (Tata McGraw – Hill, New Delhi (1994).


1. Brice J.C., Crystal growth processes – Halstead press Jhon Wiley and Sons, New

York (1986).

2. Charles P Poole Jr. and Francs J .Owens, Introduction to Nanotechnology, Wiley

(2003)

28

Hyperfine Techniques and surface spectroscopies [Effective from the academic year 2011-2012]

No. of credits: 4

No. of hours allotted: 4 / Week

Unit – 1: NMR Techniques

Quantum theory of NMR – saturation and relaxation process - Bloch equations – steady

state solutions – instrumentation block diagram - Application to molecular structure -

Chemical Shift – use of NMR in MRI .

Unit – 2: ESR Techniques

Quantum Theory of ESR – Instrumentation Technique – Block diagram – Hyperfine

Structure – Anisotropic System – Triplet state study of ESR – Application - Crystal

growth – Biological studies.

Unit – 3 : NQR Techniques

Quadrupole Hamiltonian – Nuclear quadrupole energy levels for axial and non-axial

symmetry – Experimental techniques and applications.

Unit – 4: Mossbauer Techniques

Principoles of Mossbauer spectroscopy – Chemical shirt – Quadrupole splitting and

Zeeman splitting – Simple chemical applications of Moessbauer spectroscopy.

Unit – 5: Surface Spectroscopies

Electron energy loss spectroscopy (EELS) – Reflection – Absorption – IR Spectroscopy

(RAIRS) – Inelastic Helium Scattering – Photoelectron Spectroscopy (PES) – X-Ray

(XPES) – Ultra-Violet (UPES) – Auger Electron Spectroscopy (AES).

Books for study:

1. C.N. Banwel and E.M. McCash, Fundamentals of Molecular Spectroscopy, 4th

Ed. (Tata McGraw – Hill, New Delhi (1994).

2. B.K. Sharma, Spectroscopy, Goel Publishers, Meerut, (2005).

3. G. Aruldass Molecular Structure and Spectroscopy, PHI, New Delhi, (2001)


1. Schroedinger and Berstin, High Resolution NMR (McGraw-Hill, 1959).

2. D.A. McQuarrie and J.D. Symon, Physical Chemistry-A Molecular approach

(Viva Books, New Delhi, 2001).

3. Walker and Straw, Spectroscopy, Vols I and II (Chapman and Hall, 1967).

4. R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics,

Vols. 1,2 and 3 (Narosa, New Delhi, 1998).

29

Basic Quantum Mechanics [Effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Wave-Particle Duality

Particle properties of waves: photo-electric effect and Compton effect – wave

properties of matter: deBroglie waves – phase and group velocity – experimental

evidences for matter waves: Davisson and Germer experiment and G.P. Thomson

experiment – electron microscope – Heisenberg uncertainty principle and its

consequences

UNIT 2: Schrodinger equation

Basic postulates of quantum mechanics – time independent and time dependent

Schrodinger equation – properties of wave function – probability interpretation of

wave function – probability current – normalization of wave functions and

conservation of norm – stationary states

UNIT 3: Operator formalism

Linear operators – operators associated with different observables – self-adjoint

(Hermitian) operators – expectation value – Eigen values and Eigen functions –

reality of Eigen values and Orthogonality of Eigen functions of a Hermition operator

– examples – commutativity and compatibility

UNIT 4: Angular momentum in quantum mechanics

Orbital angular momentum operators and their commutation relations – separation of

three dimensional Schrodinger equation into radial and angular parts – solution of the

angular part and spherical harmonics as the eigen functions of L2 and Lz (outline of

the steps only) – elementary ideas of spin angular momentum of an electron – Pauli

matrices

UNIT 5: Solutions of Schrodinger equation

Free particle solution – particle in a box – potential well of finite depth (one

dimension) – linear harmonic oscillator (one dimension) – rigid rotator – hydrogen

atom (only outline of steps)

30

Books for study and reference:

1. A Text book of Quantum Mechanics – P.M. Mathews and K. Venkatesan (Tata

McGraw-Hill, New Delhi, 1976)

2. Quantum Mechanics - G. Aruldhas (Prentice Hall of India, New Delhi, 2002).

3. Quantum Mechanics: Theory and applications, 4th edition – A. Ghatak and S.

Lokanathan ( Macmillar India)

4. Quantum Mechanics – E. Merzbacher, 2nd

Edition, John Wiley and Sons, New

York, 1970.

5. The Feynman Lectures on Physics – R. P. Feynman, R.B. Leighton and M. Sands,

Vol. 3, Narosa Publication, New Delhi

6. Introduction to Quantum Mechanics – Griffiths, 2nd

Edition.

31

Basic material science [Effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Introduction

Classification of materials – materials for engineering applications – different types of

chemical bonds – crystal structures of important engineering materials – crystal

imperfection and types of imperfection

UNIT 2: Phase diagram

Systems – components – phases – solid solutions – Hume-Rothery’s rule and Gibbs’

Phase rule – Lever rule – construction of phase diagrams – eutectic, peritectic, eutectoid

and peritectoid systems

UNIT 3: Phase transformation

Mechanism – nucleation and growth – applications of phase transformations – cooling,

casting, solidification and heat treatment – TTT diagram – martensitic transformation.

UNIT 4: Electron theory of metals

Classical free electron theory – density of states – electron energies in a metal – energy

band and Fermi energy in solids – distinction between metals, insulators and semi-

conductors on the basis of Fermi level – effect of temperature on Fermi level

UNIT 5: Electrical and magnetic properties of materials

Electrical resistivity and conductivity of materials – dielectric materials – electrical

polarization – piezo, pyro and ferro electric materials – electrostriction – classification of

magnetic materials – domain structure – magnetostriction – soft and hard magnetic

materials


1. Materials Science and Engineering, V. Raghavan, 4th

Ed.,Prentice-Hall India,

New Delhi, 2003.

2. Materials Science, G.K. Narula, K.S. Narula and V.K. Gupta, Tata McGraw-Hill,

1998.

3. Materials Science, M. Arumugam, 3rd

revised Ed., Anuradha Agencies, 2002.

32

Mathematical Methods [Effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Matrix theory

Types of matrices – symmetric, anti-symmetric, Hermitian and unitary matrices-Cayley-

Hamilton theorem – Proof – applications to find the inverse of a matrix – eigen values

and eigen vectors – properties of eigen values and eigen vectors of Hermitian and Unitary

matrices

UNIT 2: Tensor analysis

Definitions of covariant, contra-variant and mixed tensors – symmetric and anti-

symmetric tensors – higher order tensors – peizo-electric and moment of inertia of

tensors

UNIT 3: Special functions

Bessel’s differential equation – series solution – generating function – recurrence

relations – Hermite differential equation – series solution – Rodrigue’s formula –

generating function – recurrence relations – orthogonal property of Hermite polynomials

– Legendre differential differential equation – series solution – generating function –

recurrence relations

UNIT 4: Integral transforms

Fourier transforms – convolution theorem – properties of Fourier transforms – simple

applications – Laplace transforms – convolution theorem – properties of Laplace

transforms – simple applications

UNIT 5: Numerical methods

Solution of simultaneous linear system of equations – Gauss elimination method – matrix

inversion – Gauss-Jordan – eigen values and eigen vectors of matrices – power and

Jacobi methods


1. Matrices and Tensors in Physics, A.W. Joshi, New Age Intl., New Delhi, 1995.

2. Mathematical Physics, P.K. Chattopadhyayay, New Age Intl., New Delhi, 1990.

3. Numerical Methods, M.K. Venkatraman, National Publish. Co., Chennai

4. Mathematical Physics, Sathya Prakash, Sultan Chand & Sons, New Delhi, 1985.

33

Classical Dynamics [Effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Principles of classical mechanics

Mechanics of a single particle – mechanics of a system of particles – conservation

laws for system of particles – holonomic & non-holonomic constraints – generalized

coordinates – configuration space – transformation equations – principle of virtual

work

UNIT 2: Lagrangian formulation

D’Alembert’s principle – Lagrangian equations of motion for convervative systems –

applications: (i) simple pendulum (ii) Atwood’s machine (iii) projectile motion

UNIT 3: Hamiltonian formulation

Phase space – cyclic coordinates – conjugate momentum – Hamiltonian function –

Hamilton’s canonical equations of motion – applications: (i) simple pendulum (ii) one

dimensional simple harmonic oscillator (iii) motion of a particle in a central force

field

UNIT 4: Small oscillations

Formulation of the problem – transformation to normal coordinates – frequencies of

normal modes – linear triatomic molecule

UNIT 5: Special theory of relativity

Inertial and non-inertial frames – Lorentz transformation equations – length

contraction and time dilation – relativistic addition of velocities – Einstein’s mass-

energy relation – Minkowski’s space – four vectors – position, velocity, momentum,

acceleration and force for vector notation and their transformations


1. Classical Mechanics, H. Goldstein, 2002, Pearson education, 3rd

Ed.

2. Classical Mechanics, Upadhyaya, Himalaya Publishing co., New Delhi.

3. Introduction of Special Theory of Relativity, R. Resnick, Wiley Eastern, New

Delhi.

4. Classical Mechanics, S.N. Biswas, 1999, Books & Allied, Kolkotta.

5. Classical Mechanics, Gupta and Kumar

34

Crystal Growth Techniques

[effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Fundamentals of Crystal Growth

The Crystalline state – the birth of the concept of crystal growth – Historical review -

Importance of crystal growth – classification of crystal growth methods – Generation

of reactants – Transport of reactants to the growth surface – theories of nucleation –

homogeneous and heterogeneous nucleation – Growth surface.

UNIT 2: Growth from Low Temperature solutions

Solution – selection of solvents – solubility and super solubility – saturation and

super saturation – Meir’s solubility diagram – metastable zone width – measurement

and its enhancement – growth by restricted evaporation of solvent, slow cooling of

solution and temperature gradient methods.

UNIT 3: Growth from Flux

Flux growth – principle – choice of flux – Growth kinetics – Phase equilibrium and

phase diagram – Growth techniques – solvent evaporation techniques, slow cooling

technique and transport in a temperature gradient technique.

UNIT 4: Growth from Melt

Basis of melt growth – heat and transfer – growth techniques – conservative

processes – Bridgman-Stockbarger method – pulling from melt – Czochralski method

– zone refining – vertical, horizontal float zone methods – skull melting process.

UNIT 5: Growth from Vapour

Basic principle – physical vapour deposition – evaporation and sublimation processes

– sputtering – chemical vapour deposition – advantages and disadvantages – chemical

vapour transport – fundamentals – growth by chemical vapour transport reaction –

transported materials and transporting agents.


a. Brice J.C., Crystal growth processes – Halstead press, John Wiley and Sons,

NewYork

b. Elwell D. and Scheel H.J., Crystal growth from high temperature solutions,

Academic press, London(1975)

c. Buckley,H.E., Crystal Growth, Chapman and Hall, London(1952)

d. Ramasamy P, Crystal Growth, KPU publications, Kumbakonam.

35

Intelligent Instrumentation [Effective from the academic year 2011-2012]

No. of credits: 4


UNIT 1: Transducers and Input Elements

Classification of transducers – selecting a transducer – strain gauge – Gauge factor –

metallic sensing elements – Gauge configuration – displacement transducers – capacitive,

inductive and LVDT, peizo-electric and potentiometric transducers – thermo-couples and

thermistors – photo-sensitive devices

UNIT 2: Bridge measurements

Wheatstone bridge – Kelvin bridge – AC bridges – Maxwell bridge – K-bridge –

Schering bridge – Wien bridge – Wagner ground connection

UNIT 3: Analog and Digital principles

Operational amplifier ideal characteristics –virtual ground concept – Difference amplifier

– transducer bridge type instrumentation amplifier –digital to analog conversion –

weighted resistor type DAC – analog to digital conversion concept – flash type, counter

type and dual slope ADC – successive approximation technique ADC.

UNIT 4: Instrumentation system

Analog data – acquisition system – Digital data acquisition system – Interfacing

transducers to electronic and measuring systems – multiplexing – digital to analog

multiplexing – analong to digital multiplexing.

UNIT 5: Microprocessor based instrumentation

Programmble peripheral device 8255 – Interfacing keyboard – Matrix scanning-

Interfacing multiplexed 7 segment display – DAC and ADC interface – Waveform

generation using DAC interface- Stepper motor interface – Clockwise, anticlockwise and

wiper action- Temperature controller,-Traffic lights control.


1. Modern Electronic Instrumentation and Measurement Techniques, Albert D.

Helfrich and William D. Cooper, 5th Ed., Prentice Hall of India.

2. Integrated electronics, Milman and Halkias.

3. Digital Principles, Malvino Leech

36

4. Microprocessor architecture, programming and applications with 8085, R.S.

Gaonkar, 3rd

Ed., Penram International Publishing, Mumbai.

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