Thiagarajar college (autonomous) madurai – 9




НазваниеThiagarajar college (autonomous) madurai – 9
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Mechanics of a particle – Mechanics of a system of particles – Constraints – D’Alemberts principle and Lagrange’s equation – velocity dependent potentials and the dissipation function – Simple applications of the lagrangian formulation.


Hamilton’s principles – some techniques of the calculus of variations – Derivation of Lagrange’s equations from Hamilton’s principle – Extension of Hamilton’s principle to non – conservative and non holonomic systems – conservation theorems and symmetry properties .

UNIT II THE TWO BODY CENTRAL FORCE PROBLEM

Reduction to the equivalent one – body problem the equations of motion and first integrals. The equivalent one – dimensional problem, and classification of orbits – The viral theorem – The Kepler problem – Inverse square law of force.

UNIT III SMALL OSCILLATIONS :

Formulation of the problem – The eigen value equation and principle axis transformation – frequencies of free vibration and normal coordinates – Free vibrations of linear triatomic molecule – forced vibrations and the effect of dissipative forces.


UNIT IV THE HAMILTON EQUATION OF MOTION

Legendre transformation and the Hamilton equation of motion – Cyclic coordinates and Routh procedure – conservation theorems and the physical significance of the Hamiltonian – Derivation from variational principle – The principle of least action.
UNIT V CANONICAL TRANSFORMATIONS
The equations of canonical transformation – Examples of canonical transformations – the integral invariants of Poincare – Lagrange and Poisson brackets as canonical invariants – The equations of motion in Poisson bracket notation – Infinitesimal/constant transformations, constants of the motion and symmetry properties.

TEXT BOOK:

Classical Mechanics(III ed.), Goldtsein, H., Poole, C. & Safko, J. : Pearson Education, 2002, ISBN 81 – 7808 – 566 – 6

REFERENCE BOOKS:

  1. Mathematical Methods in Classical and Quantum Physics, Dass, T., & Sharma, S.K. : University Press, 198, ISBN 81-7371-089-9.

  2. Classical Mechanics ,Sankara Rao, K.: Prentice-Hall of India, 2005, ISBN 81-203- 2676-8.

  3. Classical Mechanics – With Introduction to Nonlinear Oscillations and Chaos, Bhatia, V.B. :, Narosa Publishing House, 1997, ISBN 81-7319-104-2.

  4. Classical Mechanics – Systems of Particles and Hamiltonian Dynamics, Greiner, W: Springer, 2004, ISBN 81-8128-128-4.

THIAGARAJAR COLLEGE – AUTONOMOUS, MADURAI – 625 009

(Re Accredited With ‘A’ Grade by NAAC)

DEPARTMENT OF PHYSICS

(From 2011 – 13 batch onwards)

Course

: M.Sc. Physics

Code :

1PP2

Semester

: I

No. of hrs. allotted :

5

Paper

: Core

No. of credits :

5

STATISTICAL MECHANICS

COURSE OBJECTIVES:

  • Fundamentals of Statistical mechanics; Statistical distribution laws; their applications.

  • Theories of specific heat capacity of solids.

  • Properties of liquid helium. Phase transitions -Ising model; discussed in detail.

UNIT I

Basis Of Classical Statistics -Phase space – Ensemble – average – Liouville theorem – Conservation of extension in phase – Equation of motion and Liouville theorem – Equal a priori probability – Statistical equilibrium – Micro canonical ensemble.

Quantum picture Micro canonical ensemble – Quantization of Phase space – Basic postulates – Classical limit – Symmetry of wave function – Effect of symmetry on counting – Various distributions using micro canonical ensemble – Density matrix.

UNIT II

Canonical And Grand Canonical Ensembles -Entropy of a system in contact with a heat reservoir – Ideal gas in canonical ensemble – Maxwell velocity distribution – Equipartition of energy – Grand canonical ensemble – Ideal gas in grand canonical ensemble – Comparison of various ensembles – Quantum distributions using other ensembles – Photons – Einstein’s derivation of Planck’s law: MASER and LASER – Equation of state for ideal quantum gases.

Partition Function Canonical partition function – Molecular partition function – Translational partition function – Rotational partition function – Vibrational partition function – Electronic and nuclear partition function – Homo nuclear molecules and nuclear spin – Application of vibrational partition function to solid – Vapour pressure.

UNIT III

Ideal Bose – Einstein Gas Bose – Einstein distribution - Bose – Einstein Condensation – Thermodynamic properties of an ideal Bose – Einstein gas – Liquid Helium – Two – Fluid model of Liquid Helium – Landau spectrum of phonons and rotons – 3He – 4He mixtures – Super fluid phases of 3He.

UNIT IV

Ideal Fermi – Dirac Gas Fermi – dirac distribution – degeneracy – Electrons in metals – Thermionic emission – White Dwarfs – Semiconductor Statistics Statistical equilibrium of free electrons in semiconductors – Nondegenerate case – Impurity semiconductors – Degenerate semiconductors.

UNIT V

Cooperative Phenomena : Ising Model Phase transitions of the second kind – Ising model – Bragg – William approximation – Fowler – Guggenheim Approximation – Kirkwood method – One-dimensional Ising model

TEXT BOOK:

Statistical mechanics (II ed.) Agarwal, B.K. & Eisner, M.:, New Age International, 2006, ISBN-81-224-1157-6.

REFERENCE BOOKS:

1. Elementary Statistical Mechanics ,Gupta, S.I & Kumar, V.:, Pragati Prakashan, 2006

2. Heat And Thermodynamics (VI ed.), Zemansky, M.W. & Dittman, R.H.: McGraw Hill, 1989. ISBN 0-07-Y66647-4.

3. Statistical Mechanics, Huang, K.: Wiley Eastern, 1988. ISBN 0-85226-393-1.

4. Thermodynamics, Kinetic Theory and Statistical Thermodynamics, Sears, F.W. & Salinger, G.L.: Narosa Publishing House, 1991. ISBN 81-85015-71-6.


THIAGARAJAR COLLEGE – AUTONOMOUS, MADURAI – 625 009

(Re Accredited With ‘A’ Grade by NAAC)

DEPARTMENT OF PHYSICS

(From 2011 – 13 batch onwards)


Course

: M.Sc. Physics

Code :

1PP3

Semester

: I

No. of hrs. allotted :

5

Paper

: Core

No. of credits :

5


ADVANCED ELECTRONICS

COURSE OBJECTIVES:

  • To be familiar with the various uses of Op-amps.

  • To relate the theory and experiments

  • To be familiar with the combinational sequential circuits

UNIT I SEMICONDUCTOR DEVICES

Field effect transistor: The ideal voltage controlled current source – the Junction Field Effect transistor – the JFET volt – ampere characteristics – JFET transfer characteristics – The MOSFET – The enhancement MOSFET – volt – ampere characteristics – The depletion MOSFET – MOSFET circuit symbols – The DC analysis of FETS – The MOSFET as a resistance – switch – amplifier – small – signal FET models – CMOS devices.

UNIT II AMPLIFIER SYSTEMS

Op.amp – architectures – The gain stage with active load – The differential stage – DC level shifting – output stages – offset voltages and currents – Measurements of op – amp parameters – Frequency response and compensation – slew rate – BIFET and BIMOS circuits - Three stage Op.amp – MOS Op amp.

UNIT III DIGITAL CIRCUITS AND SYSTEMS

Combinatorial – Digital circuits: Standard Gate assembling Binary adders – Arithmetic functions – Digital comparators – Parity checker – Generators – Decoder - Demultiplexer – Data selector – multiplexer encoder – Read only Memory (ROM) - Two dimensional addressing of a ROM – ROM applications – programmable ROMs. – Erasable PROMS ­– programmable array logic – programmable logic arrays. Sequential circuits and systems: A1 Bit memory – The circuit properties of a Bistable Latch – The clocked SR Flip flops. J - K, – T -, and D - type Flip flops – shift registers – Ripple counters – Synchronous counters – Application of counters.

UNIT IV VERY LARGE SCALE INTEGRATED SYSTEMS

Dynamic MOS shift registers – Ratioless shift register stages – CMOS Domino logic - Random Access Memory (RAM) – Read - write memory cells – Bipolar RAM cells – Charge coupled device (CCD) – CCD structures – Integrated - Injection logic(I2L) – Microprocessors and Micro computers.

UNIT V WAVE FORM GENERATORS AND WAVESHAPING

Wave form Generators and waveshaping : Sinusoidal oscillators – Phase shift: oscillator – Wien bridge oscillator – General form of oscillator configuration – crystal oscillators – multivibrators – comparator – square - wave generation from a sinusoid – Regenerative comparator – Square and triangle - wave generators – pulse generators – The 555 IC timer – voltage time - base generators – step generators – modulation of a square wave.

TEXT BOOK:

Micro Electronics (II ed.), Millman, J & Grabel, A.: Tata McGraw Hill, 2002, ISBN 0-07- 463736-3.

Unit – I Chapter- 4 ; Unit – II Chapter-14; Unit – III Chapter-7 & 8

Unit – IV Chapters-9 ; Unit – V Chapters-15


REFERENCE BOOK:

Digital Principles and application (VI ed.) Malvino, A.P. & Leech, D andGoutam Saha : Tata McGraw Hill, 2006, ISBN 0-07- 060175-5.

THIAGARAJAR COLLEGE – AUTONOMOUS, MADURAI – 625 009

(Re Accredited With ‘A’ Grade by NAAC)

DEPARTMENT OF PHYSICS

(From 2011 – 13 batch onwards)

Course

: M.Sc. Physics

Code :

1PPE1(M)

Semester

: I

No. of hrs. allotted :

5

Paper

: Elective

No. of credits :

4

MATHEMATICAL PHYSICS – I

COURSE OBJECTIVES:

  • This paper deals with the fundamental principles of electrostatics, magnetostatics and

electrodynamics.

  • Mathematical applications to physical situations in various branches of Physics like mechanics, electrostatics, electrodynamics, fluid dynamics, etc are taught.

  • Students will understand and learn the importance of application of Mathematics in solving Physical problems.

UNIT I CURVED COORDINATES, MATRICES CURVED COORDINATES:

Special coordinate systems – Circular cylindrical coordinates – Othogonal coordinates – Differential vector operators – Spherical polar coordinates – Matrices : Orthogonal matrices – Hermitian matrices and unitary matrices – Diagonalization of matrices.

UNIT II THE GAMMA FUNCTION, LEGENDRE POLYNOMIALS AND SPHERICAL HARMONICS

The Gamma function : Definition and simple properties – Digamma and polygamma functions – Legendre polynomials and spherical harmonics : Introduction – Recurence relation and special properties – Orthogonality – Alternate definitions of Legendre polynomials – Associated Legendre functions.

UNIT III BESSEL FUNCTIONS

Bessel functions of the First kind, J(x)– Asymptotic expansions – Spherical Bessel functions.

UNIT IV HERMITE AND LAGUERRE FUNCTIONS

Hermite polynomials : Quantum mechanical simple harmonic oscillator – Raising and lowering operators – Recurrence relations and generating function – Laguerre functions : Differential equation – Laguerre polynomials – Associated Laguerre polynomials.

UNIT V INTEGRAL TRANSFORMS

Introduction and Definitions – Fourier transform – Development of the inverse Fourier transform – Inversion theorem – Fourier transform derivatives – Convolution theorem – Momentum representation – Laplace transforms – Laplace transform of derivatives – Other properties.

TEXT BOOK:

Essential Mathematical Methods for Physicists, Weber, H.J. & Arfken, G.B.: Academic Press, 2004, ISBN:0-12-059878-7.

Unit I – Chapter 2, p.96-136; Chapter 3, 193-228.; Unit II – Chaper 10, p.523-540; Chapter 11, p.552-588.; Unit III – Chapters 12, p.589-637;

Unit IV – Chapter 13, p.638-662.; Unit V – Chapter 15, p.689-742.

REFERENCE BOOKS:

  1. Mathematical Methods for Physics and Engineering (II ed.), Riley, K.F., Hobson, M.P. & Bence, S.J. : Cambridge, 2004, ISBN:0-521-61296-9.

  2. S.J.: Mathematical Physics – Differential Equations and Transform Theory, Ghatak, A.K., Goyal, I.C. & Chua, Macmillan, 2002, ISBN:0-333-92548-3.

  3. Mathematical Physics (II ed.) Gupta, B.D. : Vikas Publishing House, 1993, ISBN:0-7069-76-4.

  4. Mathematical Physics (IV ed.) Satya Prakash: S. Chand & Sons, 2005, ISBN:81-7014-925-8.



THIAGARAJAR COLLEGE – AUTONOMOUS, MADURAI – 625 009

(Re Accredited With ‘A’ Grade by NAAC)

DEPARTMENT OF PHYSICS

(From 2011 – 13 batch onwards)

Course

: M.Sc. Physics

Code :

1PPE1(C)

Semester

: I

No. of hrs. allotted :

5

Paper

: Elective

No. of credits :

4


COMPUTER SIMULATIONS

COURSE OBJECTIVES:

  • To understand the importance of computers in physics.

  • To give exposure to different numerical methods.


UNIT I

Importance of Computers in Physics – Nature of Computer Simulation – Importance of Graphics – Programming Languages – Euler Algorithm – Example Coffee Cooling problem – Accuracy and stability – Visualization – Nuclear decay – Simple Harmonic Motion Motion – Numerical solution to simple harmonic oscillator of falling objects – Simple pendulum – Dissipative systems – Response to external forces – Electrical circuit oscillations

UNIT II

Chaotic motion of dynamical systems – periodic doubling – measuring and controlling chaos – Forced damped pendulum – Hamiltonian chaos – Perspective – Order – disorder – Poisson distribution and nuclear decay - introduction to0 random walks – Problems in probability – method of least squares – Simple variational Monte Carlo method – Random walks and diffusion equations.

UNIT III

Random walks, modified random walks, application to polymers, diffusion controlled chemical Numerical integration and Monte Carlo methods, numerical integration one and multi dimensional integrals, Monte carlo error, non uniform probability distributions, neutron transport, importance sampling, Metropolis Montecarlo method, error estimates for numerical integration, acceptance-rejection method, al reactions random number sequences.

UNIT IV

Percolation, cluster labeling, critical exponents and finite size scaling, renormalisation group. Fractal dimension, Regular fractals and growth processes, fractala and chaos.

UNIT V

Micro canonical ensemble, Demon alogorithm, one dimensional classical ideal gas, the temperature and the canonical ensemble, Ising model, Heat flow, relation of the mean energy to the temperature. Monte carlo simulation of canonical ensemble, Metropolis algorithm, verification of Boltzman distribution, Ising model, Ising phase transition, applications of Ising model, simulation aof classical fluids, optimized Monte Carlo data analysis, other ensembles, fluctuation in the canonical ensemble, exact enumeration of the 2 x 2 Ising model.

TEXT BOOK:

An Introduction to Computer simulation methods (Application to Physical systems) – II edition , Harvey Gould and Jan Tobochnik, Addison-Wesley Publishing Company 1996.

Unit 1: Pages 1-36, 95-126 (67 Pages)

Unit 2: Pages 127-212 (85 Pages)

Unit 3: Pages 343-405 (63 Pages)

Unit 4: Pages 413-500 (87 Pages)

Unit 5: Pages 543-625 (82 Pages)

THIAGARAJAR COLLEGE – AUTONOMOUS, MADURAI – 625 009

(Re Accredited With ‘A’ Grade by NAAC)

DEPARTMENT OF PHYSICS

(From 2011 – 13 batch onwards)


Course

: M.Sc. Physics

Code :

2PP1

Semester

: II

No. of hrs. allotted :

5

Paper

: Core

No. of credits :

5


SOLID STATE PHYSICS – I

COURSE OBJECTIVES:

  • To understand fundamentals of solid structure of materials.

  • To discuss the properties of phonons.

  • To impart the knowledge of free electron Fermi gas.

  • To give exposure to semiconductor energy bands and the methods of

calculation.


UNIT I CRYSTAL PHYSICS

Periodic arrays of atoms: Lattice translation vectors – Primitive lattice cell – Fundamental types of lattices: Two and three dimensional lattice types – Miller indices of crystal planes – Simple crystal structures : NaCl, CsCl, hcp, Diamond, Cubic ZnS – Bragg law – Fourier analysis – Reciprocal lattice vectors – Diffraction conditions – Laue equations – Brillouin zones : Reciprocal lattice to sc, bcc, fcc lattices – Structure factor of the bcc, fcc lattice, Atomic form factor – Quasi crystals


UNIT II CRYSTAL BINDING AND ELASTIC CONSTANTS

Crystals of inert gases (van der Waals – London interaction) – Ionic crystals (Madelung constant) – Covalent crystals – Metals – Hydrogen bonds – Atomic radii – Analysis of Elastic constants – Elastic compliance and stiffness constants – Elastic waves in cubic crystals.
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