Ph.D course details +++++++++++++++++++ Code : ph 801 Name: Classical Methods of Particles and Fields Credits: 8.00 Description : Particle mechanics and its applications, D`Alemberts principle, Lagrangian and Hamiltonian Mechanics, Central forces, Special theory of Relativity. Solutions of boundary value problems in Electrostatics, Green`s Functions and images, Magnetostatics, Maxwell equations and wave equations in various media, Fresnel equations. Pre-requisites : nil Text/References : H. Goldstein, C.P. Poole, J.L. Safko, Classical Mechanics, 3rd Ed., Addison Wesley, 2000. N. C. Rana and P. S. Joag, Classical Mechanics, Tata McGraw Hill, 1991. J. D. Jackson, Classical Electrodynamics, 3rd Ed., Wiley Eastern, 1985. Code : PH 802 Name: Quantum and Statistical Mechanics: Advanced Methods Credits: 8.00 Description : Review of basic concepts, Hilbert space structure of Quantum Mechanics, The free particle solution and wave packets, Uncertainty Principle and the minimum uncertainty wave packet, Single particle problems in one dimensional potentials, The WKB Formalism. Harmonic oscillator, Solution in terms of Hermite polynomials, Coherent states as minimum uncertainty wavepackets, Harmonic oscillator in algebraic language, Creation and destruction operator formalism, Angular momentum, Spherical harmonics, The same in algebraic language. Systems of identical particles, Field operator formalism for bosons and fermions, Partition function for Bose and Fermi gases, Equations of state, Degenerate Bose gas, Black body radiation, Thermodynamic properties of degenerate gas of non-relativistic Electrons, Magnetism, Generalised susceptibility, Conductivity and superconductivity. Pre-requisites : 0 Text/References : E. Merzbacher , Quantum Mechanics, 3rd Ed., John Wiley, 1998. J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley, 1994, (Indian reprint 2000) R. Shankar, Principles of Quantum Mechanics, 2nd Ed., Plenum Press, 1994. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1-2, Pergamon Press, 1980. Code : ph 803 Name: Computer Proramming and Numerical Methods Credits: 8.00 Description : Basics in computing : Basic organization of computer and its functional units; Exposure to Unix operating system. Fortran 90 programming language : Conditional statements; Looping; Logical expression and case statement; Arrays; Modular programming using functions and subroutines; Format specifications and processing strings and characters; Processing files in Fortran 90 ; Dynamic memory allocation and pointers. Numerical methods: Statistical description of data: Mean, Variance and Skewness. Solution of algebraic and transcendental equation : bisection method, the method of false position, Newton Raphson method. Interpolation. Integration of functions : Trapezoidal rule, Simpson`s 1/3 method; Least squares fit; Sorting; Matrices : Matrix inversion and evaluation of determinant by elimination method. Solution of ordinary differential equation : Runge-Kutta method, Predictor-corrector method. Random Numbers and Monte Carlo Integration. Elementary Graphics : Using gnuplot and xmgr packages to visualize data. Pre-requisites : nil Text/References : V. Rajaraman, Computer Programming in Fortran 90 and 95, Prentice Hall India, 1997. S. J. Chapman, Introduction to Fortran 90 and 95, McGraw Hill, Int. Ed., 1998 . S. E. Koonin and D. C. Meredith, Computational Physics, Addison-Wesley, 1990. W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 4th Ed, Brooks/Cole, 1999. Code : PH 804 Name: Laboratory Techniques Credits: 8.00 Description : Selected topics from the following : a) Vacuum Techniques : Production and measurement of vacuum, different typesof vacuum systems and gauges, their working and limitations, leak detection, techniques for production of ultra high vacuum. The laboratory work will consist of experiments with a vacuum system and assembling of a vacuum system. b) Electronics : Measurement techniques in electronics, use of different measuring devices, their scope and limitations. Power supplies, amplifiers, pulse techniques and high frequency techniques. Laboratory work will include handling different types of electronic measuring instruments, study of certain readymade units, design, fabrication and testing of some circuits. c) Detectors : Study of different types of detectors, photographic detectors, microwave detectors, optical detectors, X ray detectors and nuclear radiation detectors. The laboratory work will include experiments which make use of different types of detectors. d) Work Experience: Design and fabrication of simple pieces of equipments required in Physics laboratory. The students are expected to acquire familiarity with use of common machine tools like use of lathes, milling machines, drilling machines etc. Pre-requisites : - Text/References : Y. D. Lee, Particle Physics and Introduction to Field Theory, Harwood Academic Publishers, 1981. K. Huang, Quarks, Leptons and Gauge Fields, World Scientific, 1982. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw Hill, 1964. L. H. Ryder, quantum Field Theory, Cambridge University Press, 1988. Code : PH 805 Name: Application of Quantum Mechanics Credits: 8.00 Description : Review of standard methods in Quantum Mechanics including time independent perturbation theory. Selected topics from each of the parts (a), (b) and (c). a) Two electron atoms. Fermi Thomas, Hartree and Hartree Fock Equations, Configurations and spin orbit splitting. Born-Oppenheimer method for hydrogen molecule ions and hydrogenmolecule. Hydrogen atom in Dirac theory. b) Addition of angular momenta. Tensor Operators and Wigner Eckert theorem. Inter-action of radiation with matter. Ideas of quatised radiation fields. Multipole transitions. Photon scattering including Raman effect. c) Partial wave and Jost function methods in scattering. Levinson"s theorem. Varia-tional methods. Integral expressions for scattering amplitude. Born, Bethe and Oppenheimer approximations. Applications to electron-atom, ion-atom and nuclear collisions. Pre-requisites : - Text/References : J.C. Slater, Quantum Theory of Atomic structure. G. Baym, Lectures on Quantum Mechanics S. Geltman, Topics in Atomic Collision Theory Code : PH 806 Name: Special Topics in Elementary Particle Physics Credits: 8.00 Description : Phenomenology of weak, electromagnetic and strong interactions. Quantization of fields. Quantum electro-dynamics. Renomalization to one loop. Lamb shift and anomalous magnetic moment. Gauge field theories and spontaneous breaking of symmetrics. The standard model of weak, electromagnetic and strong interactions Renomalization. Pre-requisites : - Text/References : "Particle Physics and Introduction to Field Theory", Y.D. Lee, Harwood Academic Publishers, 1981. "Quarks, Leptons and Gauge Fields" K.Huang, World Scientific, 1982. "Relativisitc Quantum Mechanics" J.D. Bjorken and S.D. Drell, McGraw-Hill, 1964. "Quantum Field Theory" L.H. Ryder Cambridge University Press, 1988. Code : PH 807 Name: Current Trends in Physics Credits: 8.00 Description : The course will consist of lectures by a group of faculty on topics of current research interest in Physics. There will be three or four modules covering various areas of interest to the faculty. Pre-requisites : - Text/References : - Code : PH 808 Name: Current Trends in Physics Credits: 8.00 Description : Current Trends in Physics II same as PH-807 but covering different topics of interest. Pre-requisites : - Text/References : - Code : PH 810 Name: Advanced Simulation Techniques in Physics Credits: 8.00 Description : Basic Numerical Methods and Classical Simulations : Review of differentiation, integration (quadrature), and finding roots. Integration of ordinary differential equations. Monte Carlo simulations, applications to classical spin systems. Classical Molecular Dynamics. Quantum Simulations : Time-independent Schrodinger equation in one dimension (radial or linear equations). Scattering from a spherical potential; Born Approximation; Bound State solutions. Single particle time-dependent Schrodinger equations. Hartree-Fock Theory : restricted and unrestricted theory applied to atoms. Schrodinger equation in a basis: Matrix operations, variational properties; applications of basis functions for atomic, molecular, solid-state and nuclear calculations. Mini-projects on different fields of physics, e.g., Thermal simulations of matter using Car-Parrinello molecular dynamics; Many-Interacting-Particle Problems on Hubbard and Anderson model for electrons using Lanczos method (exact diagonalisation) for the lowest states; Quantum Monte Carlo methods; Computational methods for Lattice field theories; Microscopic mean-field theories (Hartree-Fock, Bogoliubov and relativistic mean-field); methods in nuclear many-body problems. Pre-requisites : 0 Text/References : S. J. Chapman, Introduction to Fortran 90 and 95,McGraw Hill, Int. Ed. 1998. S. E. Koonin and D. C. Meredith, Computational Physics, Addison-Wesley, 1990. Tao Pang, An Introduction to Computationl Physics, Cambridge Univ Press, 1997. R. H. Landau and M. J. P. Mejia, Computational Physics, John Wiley, 1997. J. M. Thijssen, Computational Physics, Cambridge Univ Press, 1999. K. H. Hoffmann and M. Schreiber, Computational Physics, Springer, 1996. Code : PH 811 Name: Laboratory Techniques Credits: 8.00 Description : Selected topics from the following: a) Vacuum Techniques: Production and measurement of vacuum, different types of vacuum systems and gauges, their working and limitations, leak detection, techniques for production of ultra-high vacuum. The laboratory work will consist of experiments with a vacuum system and assembling of a vacuum system. b) Electronics: Measurement techniques in electronics, use of different measuring devices, their scope and limitations. Power supplies, amplifiers, pulse techniques and high frequency techniques. Laboratory work will involve handling of different types of electronic measuring instruments. Study of certain readymade units. Design, fabrication and testing of some circuits. c) Detectors; Study of different types of detectors. Photographic detectors, micro-wave detectors, optical detectors, X-ray detectors, nuclear radiation detectors. The laboratory work will include experiments which make use of different types of detectors. d) Work Experience; Design and fabrication of simple pieces of equipment required in a physics laboratory. The students are expected to acquire familiarity with the use of common machine tools like lathes, milling machines, drilling machines, etc. Pre-requisites : - Text/References : - Code : PH 820 Name: Applications of Mathematical Techniques in Physics Credits: 8.00 Description : Application of mathematical Techniques in Physics problems in classical mechanics, electrodynamics, and quantum mechanics, based on the following topics: Vector equations; equation of motion of particles in fields. Matrices and eigenvalue problems. Differential equations. Boundary value problems. Spherical harmonics, addition theorem and multipole expansions Fourier tranforms,delta -functions, Green"s functions. Method of residues, poles and cuts in complex variables. Pre-requisites : - Text/References : G. Arfken,Mathematcial Methods of Physics Academic Press, 3rd Edn., 1985. M.L. Boas: Mathematical Methods in Physical Sciences, John Wiley, 1983 2nd Edn. Churchill, R.V., J.W. Brown and R.F. Verhey:Complex variables and applications (Mc Graw Hill) N.Y. 5th edn., 1990. Jackson J.D. Classical Electrodynamics (Wiley N.Y., 2nd Edn., 1975. Merzbacher E. Quantum Mechanics Wiley) P. Morse and H. Fesbhabch: Methods of Theoretical Physics, Vol. I II (McGraw Hill ) , 1953. Spiegel, M.R. : Schaum"s outline of theory and problems of vector analysis and an introduction to Tensor analysis, Schaum, N.Y., 1959. Stakgold I, Green Functions & Boundary Value Problems, Wiley., N.Y. M.Sc course details +++++++++++++++++++ Code : PH 403 Name: Quantum Mechanics I Credits: 8.00 Description : Historical background: Wave functions, Superposition principle, Wave packets. Schrodinger equation. Probability and current densities. Expectation values and Ehrenfest"s theorem. General formalism: Linear vectors and operators in Hillbert space, observables, commuting operators, momentum representation and uncertainty principle. Unitary transformations, Schrodinger and Heisenberg representations, Equations of motion. Applications: One dimensional potential problems, Linear harmonic oscillator polynomial solutions,creation and annihilation operators. Central forces, angular momentum, spherical harmonics, spin, addition of general angular momenta. Motion in a well. Free and bound states in a Coulomb potential. Pre-requisites : - Text/References : E. Merzbacher, Quantum Mechanics, Wiley 1970. P.M. Mathews and Venkatesan , A Text book of Quantum Mechanics, Tata McGraw Hill, 1976. A.Messiah, Quantum Mechanics, North Holland. L. Landau, and E. Lifshitz, Quantum Mechanics, Pergamon, 1956.