M.Sc. Syllabus

PH 5010 Mathematical Physics

Orthogonal and curvilinear coordinates. Scalar and vector fields, Vector differential operators: gradient, curl. divergence and Laplacian. Vector operators in curvilinear coordinates. Gauss' theorem. Green's theorem and Stokes' theorem: applications to physical problems. Tensors. Partial differential equations: applications in electrostatics, Laplace and Poisson equations: heat conduction, diffusion, elastic and electromagnetic waves. Schrodinger wave equation. Solutions in rectangular, spherical polar and cylindrical polar coordinates. Boundary conditions.

Linear vector spaces and representations. Matrices. Similarity transformations, diagonalization, orthogonality. Hermitian matrices.

Elements of complex variables. Residue theorem and contour integration.

Special functions: Bessel, Hermite, Legendre, Laugerre polynomials: generating functions and orthonormality. Addition theorem for spherical harmonics, application in heat conduction, diffusion, wave equations etc., Dirac delta function and its representations.

Fourier analysis. Fourier transforms, Laplace transforms and applications in physics.

References :

1. G. Arfken, Mathematical Methods for Physicists. Academic Press. 3rd Edition (1985).
2. I.N. Sneddon, Special Functions of Mathematical Physics and Chemistry, Longman (1980).
3. L.A. Pipes and L.R. Harwill, Applied Mathematics for Physicists and Engineers, McGraw-Hill (1971).
4. P.K. Chattopadhyay, Mathematical Physics, Wiley Eastern (1990)
5. C.R. Wylie and L.C. Barrett. Advanced Engineering Mathematics, 5th Edition, McGraw-Hill (1982).
6. E. Kreyszig, Advanced Engineering Mathematics, Wiley Eastern, Sth Edition (1991 ).
7. M.R. Spiegel in Schaum's outline series, McGraw-Hill (1964). (i) Vector Analysis (ii) Complex Variables (iii) Laplace Transforms (iv) Matrices (v) Differential Equations (vi) Group Theory.
8. H.Cohen, Mathematics for Scientists and Engineers, Prentice Hall (1992).

PH 5020 Electromagnetic Theory

Electrostatics: Laplace and Poisson equations. Boundary value problems. Dirichlet and Neumann boundary conditions. Method of images. Concept of the Green function and its use in boundary value problems. Magnetostatics: Ampere's law and Biot-Savart's law. Concept of a vector potential.

Maxwell equations and electromagnetic waves. Maxwell equations (both differential and integral formulations). Boundary conditions on field vectors D, E, B and H. Vector and scalar potentials. Gauge transformations: Lorentz and Coulomb gauges. Green function for the wave equation. Poynting's theorem. Conservation laws for macroscopic media.

Propagation of plane waves and spherical waves in free space, dielectrics and conducting media. Reflection and refraction of electromagnetic waves. Superposition of waves. Radiation from an oscillating dipole and radiation from an accelerating charge. Electromagnetic stress tensor.

Wave Guides: Modes in rectangular and cylindrical wave guides (conducting and dielectric). Resonant cavities. Evanescent waves. Energy dissipation. Q of a cavity.

References:

1. J.D. Jackson, Classical Electrodynamics, Wiley Eastern, 2nd Edition (1975).
2. David J. Griffiths, Introduction to Electrodynamics, Prentice Hall of India, 2nd Edition, (1989).
3. J.R. Reitz., F.J. Milford and R. W. Christy, Foundations of Electromagnetic Theory, 3rd Edition, Narosa Pub. House (1979).
4. P. Lorrain and D. Corson, Electromagnetic Fields and Waves. CBS Publishers and Distributors (1986).
5. B.H. Chirgwin, C. Plumpton and C. W. Kilmister, Elementary Electromagnetic Theory, Vols.1, 2 and 3" Pergamon Press (1972).

PH 5030 Classical Mechanics

Mechanics of a system of particles in vector form. Conservation of linear momentum, energy and angular momentum. Degrees of freedom, generalised coordinates and velocities. Lagrangian, action principle, external action, Euler-Lagrange equations. Constraints. Applications of the Lagrangian formalism. Generalised momenta, Hamiltonian, Hamilton's equations of motion. Legendre transform, relation to Lagrangian formalism. Phase space, Phase trajectories. Applications to systems with one and two degrees of freedom.

Central force problem, Kepler problem, bound and scattering motions. Scattering in a central potential, Rutherford formula, scattering cross section.

Noninertial frames of reference and pseudoforces: centrifugal Coriolis and Euler forces. Elements of rigid-body dynamics. Euler angles. The symmetric top. Small oscillations Normal mode analysis. Normal modes of a harmonic chain.

Elementary ideas on general dynamical systems: conservative versus dissipative systems. Hamiltonian systems and Liouville's theorem. Canonical transformations, Poisson brackets. Action-angle variables. Non-integrable systems and elements of chaotic motion.

Special relativity: Internal frames. Principle and postulate of relativity. Lorentz transformations. Length contraction, time dilation and the Doppler effect. Velocity addition formula. Four- vector notation. Energy-momentum four-vector for a particle. Relativistic invariance of physical laws.

References :

1. H. Goldstein, Classical Mechanics, 2nd Edition, Narosa Pub. House (1989).
2. I. Percival and D. Richards, Introduction to Dynamics, Cambridge University Press ( 1987) [Chapters 4,5,6, 7 in particular. also parts of Chapter 1-3,9, 10].
3. D. Rindler, Special Theory of Relativity, Oxford University Press (1982).

PH 5040 Electronics

Introduction to Integrated Circuits
Differential amplifiers using Transistors
Operational amplifiers

• Features
• Characteristics
• Negative feedback configurations
• Mathematical operations application circuits
• Non-linear applications
• Comparator
• Window comparator
• Regenerative comparator
• Relaxation oscillator
• Log and Antilog amplifiers
• Multiplier, square and square-root circuits

NE555, principle of operation and applications

Introduction to Digital logic gates 

• Combinational circuits
• Reduction using Karnaugh map
• Implementation using universal gates
• Arithmetic circuits
• Look-ahead carry implementation
• Binary BCD addition

Decoders and encoders

Multiplexers and demultiplexers their applications

Flip-flops, types and implementation

• Conversions, triggering, master/slave implementation

Registers

• Binary up down counters
• Synchronous counters
• Ring and Johnson counters

Random sequence generators

• 7-segment display devices
  

A to D and D to A converters

Applications of digital circuits

• Digital clock, stop-watch, frequency and period counter, digital voltmeter etc.

Introduction to microprocessors 

• Brief outline of 8085 processor
• Instruction set
• Simple programming examples
• Pick the largest number
• Delay
• Arithmetic operation with single and multiyear
• Block move with overlapping memory address
• Ascending and descending ordering

Test Books:

1. Electronic Principles – 5th Edition, Albert Paul Malvino
   Tana Mc-Graw-Hill Publishing Company Ltd., New Delhi, 1993
   
2. Digital Principles and Applications – 5th Edition
   Albert Paul Malvino Donald P.Lcach
   Tana Mc-Graw-Hill Publishing Company Ltd., New Delhi, 1994
3. Microprocessor Architecture, Programming and its Applications with the 8-85/8080A latest edition, 
   5th edition Ramesh S.Gaonkar 
   Wiley Eastern Ltd., New Delhi, Bangalore, Madras. , 2002
4. Digital Fundamentals – 9th edition,
   Thomas L.Floyd,
   Prentice Hall, July 13, 2005
5. Digital Design – 3rd edition,
   M.Morris Mano
   Prentice Hall, 2001
6. Digital Design – 4th edition,
   M.Morris Mano
   Prentice Hall, 2006.

PH 5080 Statistical Physics

Systems with a very large number of degrees of freedom: the need for statistical mechanics. Macrostates, microstates and accessible microstates. Fundamental postulate of equilibrium statistical mechanics.

Probability distributions. Microcanonical ensemble, Boltzmann's formula for entropy. Canonical ensemble, partition function, free energy. calculation of thermodynamic quantities. Classical ideal gas. Maxwell-Boltzmann distribution, equipartition theorem. Paramagnetism, Langevin and Brillouin functions, Curie's law.

Quantum statistics: systems of identical, indistinguishable particles, spin, symmetry of wavefunctions, bosons, Pauli's exclusion principle, fermions. Grand canonical ensemble. Bose-Einstein and Fermi-Dirac distributions. Degeneracy. Free electron gas, Pauli paramagnetism. Blackbody radiation. Bose-Einstein condensation. Einstein model of lattice vibrations. phonons, Debye's theory of the specific heat of crystals.

Phase diagrams, phase equilibria and phase transitions. Mean-fjeld theory of liquid-gas transition (Van der Waals model) and ferromagnet-paramagnet transition (Weiss' molecular field theory). Heisenberg exchange interaction and the origin of ferromagnetism. Elementary ideas on Ising and Heisenberg models of ferromagnetism.

References:

1. D. Chandler, Introduction to Modern Statistical Mechanics, Oxford University press (1987).
2. C.J. Thompson, Equilibrium Statistical Mechanics, Clarendon Press (1988).
3. F. Reif, Fundamentals of Statistical and Thermal Physics, International Student Edition, McGraw-Hill (1988).
4. K. Huand, Statistical Mechanics, IJ\Iiley Eastern (1988).
5. L.D.. Landau and E.M. Lifshitz, Statistical Physics (Par1I), 3rd Edition, Pergamon Press ( 1989).
6. F. Reif, Statistical Physics (Berkeley Physics Course, Vol.5), McGraw Hill (1967).
7. F. Mandl, Statistical Physics, 2nd edition, ELBS & Wiley (1988)
8. E.S.R. Gopal, Statistical Mechanics and Properties of Matter MacMillan India (1988).
9. R. Kubo. Statistical Physics -Problems and Solutions, North Holland (1965).
10. Y.K. Lim, Problems and Solutions in Thermodynamics and Statistical Mechanics, World Scientific (1990).

Basic principles of quantum mechanics. Probabilities and probability amplitudes. Linear vector spaces. Bra and ket vectors. Completeness, orthonormality, basis sets. Change of basis. Eigenstates and eigenvalues. Position and momentum representations. Wavefunctions, probability densities, probability current. Schrodinger equation. Expectation values. Generalized uncertainty relation.

One dimensional potential problems Particle in a box. Potential barriers. Tunnelling.

Linear harmonic oscillator: wavefunction approach and operator approach.

Motion in three dimensions. Central potential problem. Orbital angular momentum operators. Spherical harmonics. Eigenvalues of orbital angular momentum operators.

The hydrogen atom and its energy eigenvalues.

Charged particle in a uniform constant magnetic field, energy eigenvalues and eigenfunctions. Schrodinger and Heisenberg pictures Heisenberg equation of motion. Interaction picture.

Semiclassical approximation: the WKB method

Time-independent perturbation theory. Nondegenerate and degenerate cases. Examples.

Time-dependent perturbation theory. Transition probabilities. Sudden and adiabatic approximations. Fermi golden rule.

The variational method: simple examples.

References:

1. E. Merzbacher, Quantum Mechanics, 2nd Edition, Wiley International Edition (1970).
2. V.K. Thankappan, Quantum Mechanics. Wiley Eastern (1985)
3. J.J. Sakurai, Modern Quantum Mechanics, Benjamin Cummings (1985).
4. R.P. Feynman, R.B. Leighton and M.Sands, The Feynman Lectures on Physics, Vol.3, Narosa Pub. House (1992).
5. P.M. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw-Hill (1977).

PH 5110 Optics

Geometric optics: Eikonal equations, Fermat's principle and appications to laws of reflection and refraction. Parseval optics, ABCD matrix description of lenses, mirrors, etc.

Aberrations: Wavefront aberration coefficients, Transverse ray coefficients, spherical aberration, coma, astigmatism, field curvature, distortions and aberration reduction.

Dispersion: phase and group velocity, material dispersion, normal and anomalous dispersion, chromatic aberration.

Fourier techniques: Fourier analysis, Fourier transforms, diffraction of light, Fourier transformation by propagation, lenses and their description in Fourier transformation and imaging. Spread functions, modulation transfer functions, convolution, etc.

Diffraction theory of image formation, optical data processing, Coherence, classical coherence functions, autocorrelation function and time coherence. Spatial coherence, mutual coherence functions, visibility of fringes.

Crystal optics: double refraction. Polarization and anisotropy of wave propagation in crystals, dielectric and optical indicatrix, uniaxial and biaxial crystals.

Nonlinear optics susceptibility tensor and wave propagation in nonlinear media.

Waveguide optics: propogation and dispersion in cylindrical and planar waveguides.

References:

1. Max Born and Emil Wolfe, Principles of Optics, Pergamon Press, 6th Edition (1985).
2. M.V. Klein and T.E. Furtak, Optics, 2nd edition, John Wiley (1986).
3. R.S. Sirohi, Wave Optics and Applications, Orient Longman (1992)
4. A.K. Ghatak and K. Thyagarajan, Contemporary Optics, Plenum Pub. Co. (1978).
5. J.R. Mayer-Arendt M.D. Introduction to Classical and Modern Optics, 2nd Edition, Prentice Hall (1988).
6. R.S. Sirohi and M.P. Kothiyal, Optical Components, Systems and Measurement Techniques, Marcell Dekker (1991 ).
7. R.D Guenther, Modern Optics, John Wiley (1990)
8. P. Hariharan, Optical Holography, Cambridge University Press (1984).
9. D. Casasent, (ed), Optical Data Processing, Springer Verlag (1978).

PH 5120 Physics Laboratory -II

References:

• Worsnop and Flint, Advanced Practical Physics for Students Methusen & Go. (1950).
• E.V. Smith, Manual for Experiments in Applied Physics. Butterworths (1970).
• R.A. Dunlap, Experimental Physics: Modern Methods, Oxford University Press (1988).
• D. Malacara (ed), Methods of Experimental Physics, Series of Volumes, Academic Press Inc. (1988).

PH 5160 Condensed Matter Physics-I

Classification of condensed matter: crystalline, noncrystalline, nanophase solids, liquids. Crystalline solids: Bravais lattices, crystal systems, point groups, space groups and typical structures.

Crystal symmetry and macroscopic physical properties: tensors of various ranks: pyroelectricity, ferroelectricity, electrical conductivity, piezoelectricity and elasticity tensors. Propagation of elastic waves in crystals and measurement of elastic constants.

Diffraction of waves by crystals: X-rays, neutrons, electrons. Bragg's law in direct and reciprocal lattice. Structure factor. Principles of diffraction techniques. Brillouin zones.

Types of binding. Ionic crystals: Born Mayer potential. Thermochemical Bom-Haber cycle. Van der Waals binding: rare gas crystals and binding energies. Covalent and metallic binding: characteristic features and examples.

Lattice dynamics: monoatomic and diatomic lattices. Born-von Karman method. Phonon frequencies and density of states. Dispersion curves, inelastic neutron scattering. Reststrahlen Specific heat. Thermal expansion. Thermal conductivity. Normal and Umklapp processes.

Free electron theory of metals. Thermal and transport properties. Hall effect Electronic specific heat.

Bloch functions. Nearly free electron approximation. Formation of energy bands. Gaps at Brillouin zone boudaries. Electron states and classification into insulators, conductors and semimetals. Effective mass and concept of holes. Fermi surface. Cyclotron resonance.

Semiconductors: carrier statistics in intrinsic and extrinsic crystals, electrical conductivity. Liquid crystal: thermotropic and lyotropic. Nematics and sematics: applications. Amorphous/glassy states.

References:

1. Charles Kittel, Introduction to Solid State Physics, Wiley, 5th Edition ( 1976).
2. A.J. Dekker. Solid State Physics, Prentice Hall, (1957)
3. N.W. Ashcroft and N.D. Mermin, Solid State Physics, Saunders College Publishing (1976).
4. J.S. Blakemore,Solid State Physics, 2nd Edition, Cambridge University Press. (1974).
5. Mendel Sachs, Solid State Theory, McGraw-Hill (1963)
6. Harald bach and Hans Luth, Solid-State Physics, Springer International Student Edition, Narosa Pub. House, (1991).

PH 5170 Quantum Mechanics-II

Orbital and spin angular momentum. Angular momentum algebra. Eigenstates and eigenvalues of angular momentum. Addition of angular momenta, Clebsch-Gordon coefficients. Irreducible tensor operators and the Wigner-Eckart theorem.

Systems of identical particles. Symmetric and antisymmetric wavefunctions. Bosons and Fermions. Pauli's exclusion principle. Second quantization, occupation number representation.

Non-relativistic scattering theory. Scattering amplitude and cross- section. The integral equation for scattering. Born approximation. Partial wave analysis. The optical theorem.

Elements of relativistic quantum mechanics. The Klein-Gordon equation. The Dirac equation. Dirac matrices, spinors. Positive and negative energy solutions, physical interpretation. Nonrelativistic limit of the Dirac equation.

References:

1. J.J. Sakurai Modern Quantum Mechanics, Benjamin / Cummings (1985).
2. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1991 ).
3. L.D.Landau and E.M. Lifshitz, Quantum Mechanics -Nonrelativistic Theory, 3rd Edition, Pergamon (1981 ).
4. P.M. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw-Hill (1977).
5. J. Bjorken and S. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1965).
6. A. Messiah, Quantum Mechanics, Vols. 1 and 2, North Holland (1961 )

PH 5210 Condensed Matter Physics -II

Internal electric field in a dielectric. Clausius-Mossotti and Lorentz-Lorenz equations. Point dipole, deformation dipole and shell models. Dielectric dispersion and loss. Ferroelectrics: types and models of ferro electric transition.

Diamagnetic susceptibility. Quantum theory of paramagnetism. Transition metal ions and rare earth ions in solids. Crystal field effect and orbital quenching. Ferromagnetic and antiferromagnetic ordering. Curie-Weiss theory, Heisenberg theory, Curie and Neel temperatures. Domain walls, Spin waves and magnon dispersion.

Optical properties of solids: band to band absorption, excitons. polarons. Colour centres. Luminescence. Photoconductivity. Point defects: Thermodynamics of point defects. Frenkel and Schottky defects. Formation enthalpies. Diffusion and ionic conductivity. Superionic materials.

Extended defects: dislocations, models of screw and edge dislocations. Burgers vector. Stress field around dislocations, interaction between dislocations with point defects. Work hardening.

Superconductivity, experimental and theoretical aspects, new materials and models.

Referenes:

1. Charles Kittel, Introduction to Solid State Physics, Wiley, 5th Edition, (1976).
2. A.J. Dekker, Solid State Physics, Prentice Hall (1957).
3. N.W. Ashcroft and N.D. Mermin, Solid State Physics, Saunders College Publishing (1976).
4. J.S. Blakemore, Solid State Physics, 2nd Edition, Cambridge University Press, (1974).
5. Mendel Sachs, Solid State Theory, McGraw-Hill (1963).
6. A.O.E. Animalu, Intermediate Quantum Theory of Solids, Prentice Hall (1977).

PH 6110 Classical Field Theory

Lorentz transformations: infinitesimal generators, metric tensors, the light cone. Contravariant and covariant vectors and tensors.

Classical field theory of a real scalar field: action, Lagrangian density, Euler-Lagrange field equation. The conjugate momentum. Hamiltonian density, energy-momentum tensor, physical interpretation .

Angular momentum tensor for a real scalar field. Invariance under Lorentz transformations and conservation of angular momentum. Internal degrees of freedom and symmetrization of the energy-momentum tensor.

complex scalar field :Lagrangian, field equations, global field invarience.

Noether's theorem: transformations, invariance and conserved quantities. Translations, rotations, Lorentz and gauge transformations as illustrations.

The mass less vector field: Lagrangian, field equations, Lorentz condition. The field tensor, Maxwell's equations. Energy density, Poynting vector. Invariance of the electromagnetic field. Lorentz transformation properties of electric and magnetic fields. Minimal coupling of matter fields to the electromagnetic field. Covariant derivative, local gauge invariance, continuity equation for the current, charge conservation.

General covariance. Curved space, metric tensor, connection, parallel transport, covariant derivative, curvature tensor. Principle of equivalence. Gravitational field equations.

References:

1. L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields, 4th Edition, Pergamon (1975).
2. M.R. Spiegel. Vector Analysis, Schaum Outline Series, McGraw-Hill (1974).
3. M. Carmeli, Classical Fields, Wiley (1982).
4. A.O. Barut, Electrodynamics and Classical Theory of Fields, Chapter 1, MacMillan (1986).
5. C. Itzykson and J.8. Zuber, Quantum Field Theory, International Student Edition, Chapter 1 (1986).