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Old April 2nd, 2014, 06:16 PM
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Default Re: IISC Syllabus of Integrated Ph.D course (Physics)

As you need the IISC Syllabus of Integrated Ph.D course (Physics), here I am sharing the same:

Course Credits Course Title
PH 201 3:0 Classical Mechanics
PH 202 3:0 Statistical Mechanics
PH 203 3:0 Quantum Mechanics I
PH 204 3:0 Quantum Mechanics II
PH 205 3:0 Mathematical Methods of
Physics
PH 206 3:0 Electromagnetic Theory
PH 207 1:2 Analog Digital and
Microprocessor Electronics
PH 208 3:0 Condensed Matter Physics-I
PH 209 2:1 Analog and Digital Electronics
Lab
PH 211 0:3 General Physics Laboratory
PH 212 0:3 Experiments in Condensed
Matter Physics
PH 213 0:4 Advanced Experiments in
Condensed Matter Physics
PH 215/
HE 215 3:0 Nuclear and Particle Physics
PH 217 3:0 Fundamentals of Astrophysics
PH 231 0:1 Workshop practice
PH 300 1:0 Seminar Course

IISC Syllabus of Integrated Ph.D course (Physics)

PH 201 (AUG) 3:0
Classical Mechanics

Newton’s laws, generalised co-ordinates. Lagrange’s principle of least action and equations. Conservation laws and symmetry. Integrable problems, elastic collisions and scattering. Small oscillations including systems with many degrees of freedom, rigid body motion. Hamilton’s equations. Poisson brackets. Hamilton Jacobi theory. Canonical perturbation theory, chaos, elements of special relativity. Lorentz trans-formations, relativistic mechanics.

Vasant Natarajan and K P Ramesh

Goldstein, H., Classical Mechanics, Second Edn, Narosa, New Delhi, 1989.
Landau, L.D., and Lifshitz, E.M., Mechanics, Pergamon, UK, 1976.
Rana, N.C., and Joag, P.S., Classical Mechanics Tata McGraw-Hill, New. Delhi, 1991.

PH 202 (JAN) 3:0
Statistical Mechanics

Basic principles of statistical mechanics and its application to a few simple systems. Probability theory, fundamental postulate, phase space, Liouville’s theorem, ergodicity, microcanical ensemble, connection with thermodynamics, canonical ensemble, classical ideal gas, harmonic oscillators, paramagnetism, Ising model, physical applications to polymers, biophysics. Grand canonical ensemble, thermodynamic potentials, Maxwell relations, Legendre transformation, introduction to quantum statistical mechanics, Fermi, Bose and Boltzmann distribution, Bose condensation, photons and phonons, Fermi gas, classical gases with internal degrees of freedom, fluctuation, dissipation and linear response, Monte Carlo and molecular dynamics methods.

H R Krishnamurthy

Pathria, R.K., Statistical Mechanics, Butterworth Heinemann, Second Edn, 1996.
Reif, F., Fundamentals of Statistical and thermal Physics, McGraw Hill, 1965.
Huang, K., Statistical Mechanics,
Bhattacharjee, J.K., Statistical Mechanics: Equilibrium and non-equilibrium aspects.
J P Sethna, J.P., Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford Univ Press, 2006.


PH 203 (AUG) 3:0
Quantum Mechanics-I

Examples of probability amplitudes and superposition. Preparation, measu-rement, and evolution of states in a two level systems, e.g polarised light, Stern Gerlach experiments. Matrix formulation of quantum theory. Unitary andHermitean operators and the properties. Wave functions for a single particle. Momentum operator and representation. Time evolution, the Hamiltonian, Schrodinger equation. Probability current, wave packets, uncertainty principle, classical limit. Stationary states, their orthogonality and completeness. Variational methods. One dimensional problems – bound states, tunneling, scattering. The harmonic oscillator, analytical and operator approaches. Three dimensional problems. Symmetries, conservation laws, degeneracies, with examples. Infinitesimal rotations, angular momentum operators, commutation relations and their consequences. Separation of variables for a central force problem. Spherical harmonics. The hydrogen atom. Alkali atoms. The spin orbit and hyperfine interactions. Time independent perturbation theory, non-degenerate and degenerate cases. Fine and hyperfine structure of energy levels.Stark and Zeeman effects.

Sriram Ramaswamy

Cohen-Tannoudji, C., Diu, B., and Laloe, F., Quantum Mechanics Vol.1, John Wiley & Sons, 1977.
Merzbacher, E., Quantum Mechanics, John Wiley & Sons, 1968.
Thankappon, V.K., Quantum Mechanics, Wiley Eastern Ltd., 1993.

PH 204 (JAN) 3:0
Quantum Mechanics II

Time dependent perturbation theory. Fermi golden rule. Transitions caused by a periodic external field. Dipole transitions and selection rules. Decay of an unstable state. Born cross section for weak potential scattering. Adiabatic and sudden approximations. WKB method for bound states and tunneling. Scattering theory: partial wave analysis, low energy scattering, scattering length, born approximation, optical theorem, Levinson’s theorem, resonances, elements of formal scattering theory. Minimal coupling between radiation and matter, diamagnetism and paramagnetism of atoms, Landau levels and Aharonov Bohm effect. Addition of angular momenta, Clebsch Gordon series, Wigner Eckart theorem, Lande’s g factor. Many particle systems: identity of particles, Pauli principle, exchange interaction, bosons and fermions. Second quantization, multielectron atoms, Hund’s rules. Binding of diatomic molecules. Introduction to Klein Gordon and Dirac equations, and their non relativistic reduction, g factor of the electron.

Chandan Dasgupta

Landau, L.D., and Lifshitz E.M., Quantum Mechanics, Pergamon, NY, 1974.
Baym, G., Lectures on Quantum Mechanics, Benjamin, NY, 1973.
Bethe, H.A., and Jackiw, R., Intermediate Quantum Mechanics, Benjamin, NY, 1968.


PH 205 (AUG) 3:0
Mathematical Methods of Physics

Linear vector spaces, linear operators and matrices, systems of linear equations. Eigen values and eigen vectors, classical orthogonal polynomials. Linear ordinary differential equations, exact and series methods of solution, special functions. Linear partial differential equations of physics, separation of variables method of solution. Complex variable theory; analytic functions. Taylor and Laurent expansions, classification of singularities, analytic continuation, contour integration, dispersion relations. Fourier and Laplace transforms.

Diptiman Sen

Mathews, J., and Walker, R.L., Mathematical Methods of Physics, Benjamin, Menlo Park, California, 1973.
Dennery, P., and Krzywicki, A., Mathematics for Physicists, Harper and Row, NY, 1967.
Wyld, H.W., Mathematical Methods for Physics, Benjam, Reading, Massachusetts, 1976.


PH 206 (JAN) 3:0
Electromagnetic Theory

Laws of electrostatics and methods of solving boundary value problems. Multipole expansion of electrostatic potentials, spherical harmonics. Electostatics in material media, dielectrics. Biot-Savart Law, magnetic field and the vector potential. Faraday’s Law and time varying fields. Maxwell’s equations, energy and momentum of the electromagnetic field, Poynting vector, conservation laws. Propagation of plane electromagnetic waves. Radiation from an accelerated charge, retarded and advanced potentials, Lienard-Wiechert potentials, radiation multipoles. Special theory of relativity and its application in electromagnetic theory. Maxwell’s equations in covariant form: four – potentials, electromagnetic field tensor, field Lagrangian. Elements of classical field theory, gauge invariance in electromagnetic theory.

Arnab Rai Choudhuri

Jackson, J.D., Classical Electrodynamics, Third Edn, John Wiley.
Panofsky, W.K.H., and Phillips, M., Classical Electricity and Magnetism, Second Edn, Dover.

PH 207 (JAN) 1:2
Electronics – I

Basic diode and transistor circuits, operational amplifier and applications, active filters, voltage regulators, oscillators, digital electronics, logic gates, Boolean algebra, flip-flops, multiplexers, counters, displays, decoders, D/A, A/D. Introduction to microprocessors.

V Venkataraman

Horowitz and Hill, The Art of Electronics, Second Edn.
Millman and Halkias, Integrated Electronics, McGraw Hill.
Gayakwad, R., Operational amplifiers and Linear Integrated Circuits.Publishers?

PH 208 (JAN) 3:0
Condensed Matter Physics I

Drude model, Sommerfeld model, crystal lattices, reciprocal lattice, x-ray diffraction, Brillouin zones and Fermi surfaces, Bloch’s theorem, nearly free electrons, tight binding model, selected band structures, semiclassical dynamics of electrons, measuring Fermi surfaces, cohesive energy, classical harmonic crystal, quantum harmonic crystal, phonons in metals, semiconductors, diamagnetism and paramagnetism, magnetic interactions.

Arindam Ghosh

Ashcroft, N.W., and Mermin, N.D., Solid State Physics, Holt-Saunders International, NY, 1976.
Kittel, C., Introduction to Solid State Physics, 5th/6th/7th editions, Wiley International, Singapore.


PH 209 (AUG) 2:1
Analog and Digital Electronics Laboratory

Introduction to microprocessors, Intel 80x86 architecture, instruction set. Assembly and C level programming, memory and IO interfacing. Mini projects using integrated circuits, Data acquisition systems. PC Add-on boards.Introduction to Virtual Instrumentation.

K Rajan and K S Sangunni

Hall, DV., Digital circuits and systems, McGraw Hill International Electronic Engineering Series.
Hall, DV., Microprocessors and Interfacing, Second Edn, Tata McGraw Hill.
Robert Bishop, Learning with LabView Express, Pearson Edn.

PH 211 (AUG) 0:3
General Physics Laboratory

Diffraction of light by high frequency sound waves, Michelson interferometer, Hall effect, band gap of semiconductors, diode as a temperature sensor, thermal conductivity of a gas using Pirani gauge, normal modes of vibration in a box, Newton’s laws of cooling, dielectric constant measurements of triglycine selenate, random walk in porous medium.

Vasant Natarajan, K P Ramesh and Prasad V Bhotla

PH 212 (JAN) 0:3
Experiments in Condensed Matter Physics
Hall coefficient carrier mobility and life-time in semiconductors, resistivity measurement in anisotropic materials, crystal growth, crystal optics, light scattering, electron tunnelling, resonance spectroscopy, coexistence curve for binary liquid mixtures, magnetic susceptibility, dielectric loss and dispersion. Meissner fraction of a high temperature superconductor, the specific heat of a glass, microwave and rf absorption in high Tc materials, surface studies by STM in air, electron tunneling/STM magnetic susceptibility, calibration of a cryogenic temperature sensor (oxide/Ge sensor), resistivity vs temperature of a superconductor.

Reghu Menon, Suja Elizabeth and D V S Muthu

Weider, Lab. notes of electrical measurements.
Smith and Richardson, Experimental methods in low temperature physics.


PH 213 (AUG) 0:4
Advanced Experiments in Condensed Matter Physics

This lab course has two components: In the first part, the students will do the following five experiments in the Central Instruments Facility of the department to learn about the basic preparation characterization tools.

1. Laue diffraction
2. Powder diffraction
3. Differential Scanning calorimetry
4. Optical absorption spectra
5. RF sputtering
In the second part the students will do an 8 weeks project in a designated lab under the supervision of a faculty member. Such projects will be floated at the beginning of the semester and students will have to choose from among the available projects.

Ramesh C Mallik, Prasad V Bhotla and V. Venkataraman


HE 215 / PH 215 (AUG) 3:0
Nuclear and Particle Physics

Radioactive decay, subnuclear particles. Binding energies. Nuclear forces, pion exchange, Yukawa potential. Isospin, neutron and proton. Deuteron. Shell model, magic numbers. Nuclear transitions. Selection rules. Liquid drop model. Collective excitations. Nuclear fission and fusion. Beta decay. Neutrinos. Fermi theory, parity violation, V-A theory. Mesons and baryons. Lifetimes and decay processes. Discrete symmetries, C, P, T and G. Weak interaction transition rules. Strangeness, K mesons and hyperons. Composition of mesons and baryons, quarks and gluons.

B Ananthanarayan

Povh, B., Rith, K., Scholz, C., and Zetsche, F., Particles and Nuclei, An Introduction to Physical Concepts, Second Edn, Springer, 1999.
Krane, K.S., Introductory Nuclear Physics, John Wiley and Sons, NY, 1988.
Griffiths, D., Introduction to Elementary Particles John Wiley and Sons, NY, 1987.
Perkins, D.H., Introduction to High Energy Physics, Third edition, Addison-Wesley, Reading, 1987.

PH 217 (AUG) 3:0
Fundamentals of Astrophysics

Overview of the major contents of the universe. Basics of radiative transfer and radiative processes. Stellar interiors. HR diagram. Nuclear energy generation. White dwarfs and neutron stars. Shape, size and contents of our galaxy.Basics of stellar dynamics. Normal and active galaxies. High energy and plasma processes. Newtonian cosmology. Microwave background. Early universe.

B Mukhopadhyay

Choudhuri, A.R., Astrophysics for Physicists
Shu, F., The Physical Universe.
Shapiro, S.L., and Teukolsky, S.A., Black Holes, While Dwarfs, and Neutron Stars: The Physics of Compact Objects
Carroll, B.W., and Ostlie, D.A., Introduction to Modern Astrophysics.

PH 231 (AUG) 0:1
Workshop practice

Use of lathe, milling machine, drilling machine, and elementary carpentry Working with metals such as brass, aluminium and steel.

K S Sangunni

PH 250A (JAN) 0:6
Project – I

PH 250B (MAY) 0:6
Project – II

This two part project is offered by the faculty members of the department. It starts in the fourth semester of the Integrated Ph.D Programme (PH 250 A) and ends in the summer before the beginning of the 5th semester (PH 250B).



PH 300 (AUG) 1:0
Seminar Course

The course aims to help the fresh research student in preparing, presenting and participating in seminars. These seminars are run in a course form after proper guidance by the instructors, They will be given by the students who register for this course.

Vijay Shenoy and Arindam Ghosh



HE 316 / PH 316 (JAN) 3:0
Advanced Mathematical Methods

Introduction to finite and continuous groups. Group representations and operations on them. Permutation group and its representations. Lie groups and Lie algebras. SU(2), SU(3) and SU(N) groups. Roots and weights. Lorentz and Poincare groups. Introduction to manifolds, differential geometry, fibre bundles, topology and homotopy.

Aninda Sinha

Hamermesh, M., Group Theory and its Applications to Physical Problems, Addison-Wesley, Reading, 1962.
Mukhi, S., and Mukunda, N., Introduction to Topology, Differential Geometry and Group Theory for Physicists, Wiley Eastern, 1990.
Nash, C., and Sen, S., Topology and geometry for physicists, Academic Press, 1988.
Schutz, B. F., Geometrical Methods of Mathematical Physics, Cambridge University Press, 1980.


PH 320 (AUG) 3:0
Condensed Matter Physics - II

Review of one-electron band theory. Effects of electron-electron interaction: Hartree – Fock approximation, exchange and correlation effects, density functional theory, Fermi liquid theory, elementary excitations, quasiparticles.Dielectric function of electron systems, screening, plasma oscillation. Optical properties of metals and insulators, excitons. The Hubbard model, spin-and charge-density wave states, metal-insulator transition. Review of harmonic theory of lattice vibrations. Anharmonic effects. Electron-phonon interaction – phonons in metals, mass renormalization, effective interaction between electrons, polarons. Transport phenomena, Boltzmann equation, electrical and thermal conductivities, thermo-electric effects. Superconductivity–phenomenology, Cooper instability, BCS theory, Ginzburg-Landau theory.

Subroto MukerjeePH

Ashcroft, N.W., and Mermin, N.D., Solid State Physics, Saunders College, Philadelphia.
Madelung, O., Introduction to Solid State Theory, Springer-Verlag, Berlin.
Jones, W., and March, N.H., Theoretical Solid State Physics, Dover Publications, New York.



PH 322 (JAN) 3:0
Molecular Simulation

Introduction to molecular dynamics, various schemes for integration, inter- and intra-molecular forces, introduction to various force fields, methods for partial atomic charges, various ensembles (NVE, NVT, NPT, NPH), hard sphere simulations, water imulations, computing long-range interactions. Various schemes for minimization: conjugate radient, steepest descents. Monte Carlo simulations, the Ising model, various sampling methods, particle-based MC simulations, biased Monte Carlo. Density functional theory, free energy calculations, umbrella sampling, smart Monte Carlo, liquid crystal simulations. Introduction to biomolecule simulations.

Prabal K Maiti

Prerequisites: Basic courses in statistical physics, quantum mechanics

Frenkel, D., and Smit, B., Understanding Molecular Simulation, Academic Press, NY, 2001.
Allen, M.P., and Tildesley, D.J., Computer Simulation of Liquids, Oxford Science, 2002.


PH 325 (AUG) 3:0
Advanced Statistical Physics

Systems and phenomena. Equilibrium and nonequilibrium models. Techniques for equilibrium statistical mechanics, with examples, e.g., exact solution, mean field theory, perturbation expansion, Ginzburg Landau theory, scaling, numerical methods. Critical phenomena, classical and quantum. Disordered systems including percolation and spin glasses. A brief survey of non-equilibrium phenomena including transport, hydrodynamics, and non-equilibrium steady states.

Rahul Pandit

Chaikin, P.M., and Lubensky, T.C., Principles of Condensed Matter Physics, Cambridge University Press, 1995.
Plischke, M., and Bergersen, B.. Equilibrium Statistical Physics, Second Edn, World Scientific, 1994.
Sethna, J.P., Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford Univ. Press, 2006.

PH 330 (AUG) 0:3
Advanced Independent Project In Physics
(open to research students only)

Faculty

PH 347 (AUG) 2:0
Bioinformatics

Biological databases: Organisation, searching and retrieval of information, accessing global bioinformatics resources using the World Wide Web. UNIX operating system and network communication. Nucleic acid sequence assembly, restriction mapping, finding simple sites and transcriptional signals, coding region identification. Similarity and homology, dotmatrix methods, dynamic programming methods, scoring systems, multiple sequence alignments, evolutionary relationships, genome analysis. Protein structure classification, secondary structure prediction, hydrophobicity patterns, detection of motifs, structural databases (PDB), genome databases, structural bioinformatics. Biological systems.
Topics from the current literature will be discussed. Hands on experience will be provided.

S Ramakumar and K Sekar

Mount, D.W., Bioinformatics: Sequence and Genome Analysis, Second Edn, Cold Spring Harbor Laboratory Press, 2005.
Zvelebil, M., and Baum, J.O., Understanding Bioinformatics, Garland Science, 2008.
Pevsner, J., Bioinformatics and Functional Genomics, Second Edition, Wiley-Blackwell, 2009.




PH 350 (JAN) 3:0
Physics of Soft Condensed Matter

Phases of soft condensed matter; colloidal fluids and crystals; polymer solutions, gels and melts; micelles, vesicles, surfactant mesophases; polymer colloids, microgels and star polymers - particles with tunable soft repulsive interaction, surfactant and phospolipid membranes; lyotropic liquid crystals. Structure and Dynamics of soft matter; electrostatics in soft matter, dynamics at equilibrium; glass formation and jamming, dynamical heterogeneity. Soft glassy rheology; shear flow, linear and non-linear rheology; visco-elastic models; Introductory Biological Physics; Active matter.
Experimental methods; Small angle scattering and diffraction, Dynamic light scattering and diffusive wave spectroscopy; methods for studying dynamics of soft matter using synchrotron x-ray and neutron scattering; rheometry;confocal microscopy.

Prerequisite: Knowledge of basic statistical mechanics

Jaydeep K Basu and Sriram Ramaswamy

Jones, R.A.L., Soft Condensed Matter, Oxford University Press, 2002.
Rubinstein, M., and Colby, R.H., Polymer physics, Oxford, 2003.
Doi and Edwards, Theory of Polymer Dynamics, Clarendon, Oxford, 1988.
Philip Nelson, Biological Physics: Energy, Information and Life, Freeman, 2003.
Phillips, R., Kondev, J., and Theriot, J., Physical Biology of the Cell, Garland Science, 2008.
Israelachvilli, J.N., Intermolecular and surface forces, Second Edn, Academic press London, 1992.
W B Russel et al., Colloidal Dispersions, Cambridge Univ. Press, 1989.
Safran, S., Statistical thermodynamics of surfaces, interfaces and membranes, Addison-Wiley, Mass. 1994.
Gelbart, Roux and Ben-Shaul, Micelles, Membranes, Micremulsions and Monolayers, Springer, NY, 1994.
Chaikin, P.M., and Lubensky, T.C., Principles of condensed matter physics, Cambridge Univ. Press, New Delhi, 1998.
P-G de Gennes, Prost, J., The physics of liquid crystals, Clarendon, Oxford, 1995.




PH 351 (AUG) 2:0
Crystal Growth and Characterization

Basic concepts: nucleation phenomena, mechanisms of crystal growth, dislocations and crystal growth, crystal dissolution, materials preparation and phase diagrams. Experimental methods of crystal growth: growth from liquid-solid equilibria, growth from vapour-solid equilibria, mono-component and multi-component techniques. Special techniques: Thin film growth methods including LPE, MOCVD, MBE, PLD, etc. Crystal characterization.

Suja Elizabeth

Laudise, R.A., Growth of Single Crystals, Prentice-Hall, 1970.
Brice, J.C., Crystal Growth Process, John Wiley, 1988.
Hurle, D.T.J., (ed.), Handbook of Crystal Growth, Ed., North Holland, 1994.


PH 352 (JAN) 3:0
Semiconductor Physics and Technology

Semiconductor fundamentals: band structure, electron and hole statistics, intrinsic and extrinsic semiconductors, energy band diagrams, drift-diffusion transport, generation- recombination, optical absorption and emission. Basic semiconductor devices: on junctions, bipolar transistors, MOS capacitors, field-effect devices, optical detectors and emitters. Semiconductor technology: fundamentals of semi- conductor processing techniques; introduction to planar technology for integrated circuits.

K S R Koteshwara Rao

Seeger, K., Semiconductor Physics, Springer-Verlag, 1990.
Sze, S.M., Physics of Semiconductor Devices, Wiley, 1980.
Muller, K., and Kamins, T., Device Electronics for Integrated Circuits, John Wiley and Sons, 1977.
Lee, H.H., Fundamentals of Microelectronics Processing, McGraw Hill, 1985.


PH 359 (JAN) 3:0
Physics at the Nanoscale

Introduction to different nanosystems and their realization; electronic properties of quantum confined systems: quantum wells, wires, nanotubes and dots. Optical properties of nanosystems: excitons and plasmons; photoluminescence, absorption spectra, vibrational and thermal properties of nanosystems; zone folding. Raman characterization.

A K Sood

Nanostructures: Theory and Modelling, by C. Delerue and M Lannoo, (Springer, 2006), by Saito, R., Dresselhaus, G., and Dresselhaus, M.S., Physical Properties of Carbon Nanotubes, Imperial College Press.




HE 392/PH 392 (AUG) 3:0
Standard Model of Particle Physics
Weak interactions before gauge theory, V-A theory, two component neutrino, massive vector bosons. Spontaneous symmetry breaking (U(1)/SU(2)), Higgs mechanism and mass bounds, custodial symmetry, SU(2) X U(1)Lagrangian, GIM mechanism, CP-violation, particle-antiparticle mixing: K/B systems, S,T,U parameters and precision measurements. Topics in QCD: asymptotic freedom, operator product expansion, deep inelastic scattering and Parton model.

N D Hari Dass and B Ananthanarayan

Cheng, T.P., and Li, L.F., Gauge Theory of Elementary Particle Physics, Oxford University Press, 1988.
Commins, E.D., and Bucksbaum, P.H., Weak Interactions of Leptons and Quarks, Cambridge University Press, 1983.
Peskin, M.E., and Schroeder, D.V., An introduction to quantum field theory, Addison-Wesley, 1995.
Quigg, C., Gauge Theories of the Strong, Weak and Electromagnetic Interactions, Benjamin-Cummings, 1983.
Georgi H., Weak Interactions and Modern Particle Theory, Benjamin-Cummings, 1984. Donoghue, J.F., Golowich, E., and Holstein, B.R., Dynamics of the Standard Model, Cambridge U.P., 1998.
Sterman, G., An Introduction to Quantum Field Theory, Cambridge University Press, 1993.

HE 395/PH 395 (AUG) 3:0
Quantum Mechanics III

Relativistic quantum mechanics, Klein-Gordon and Dirac equations. Antiparticles and hole theory. Nonrelativistic reduction. Discrete symmetries P, C and T. Lorentz and Poincare groups. Weyl and Majorana fermions. Scalar fields, Dirac fields. Canonical quantisation. Propagators. Interactions and Feynman diagrams. S-matrix. Scattering cross sections, decay rates and non-relativistic potentials. Loop diagrams and renormalisation. Power counting andrenormalisability. Global and local symmetries. Noether theorem.

Sudhir Vempati

Bjorken, J.D., and Drell, S., Relativistic Quantum Mechanics, McGraw-Hill, 1965.
Peskin, M.E., and Schroeder, D.V., An Introduction to Quantum Field Theory, Addison Wesley, 1995.
Ryder, L.H., Quantum Field Theory, Cambridge University Press, 1985.
Sakurai, J.J., Advanced Quantum Mechanics, Benjamin Cummings, 1967.


HE 396 / PH 396 (JAN) 3:0
Gauge Field Theories

Path integral formulation, generating functional. Grassmann path integrals. Yukawa theory. Abelian gauge theories. QED processes and Ward identities. Loop diagrams and renormalisation. Lamb shift and anomalous magnetic moment. Nonabelian gauge theories. Spontaneous symmetry breaking, Goldstone bosons. Faddeev-Popov ghosts. Callan-Symanzik equation, beta function. Asymptotic freedom.

Sudhir Vempati

Cheng, T.P., and Li, L.F., Gauge Theories of Elementary Particle Physics, Clarendon, 1984.
Pokorski, S., Gauge Field Theories, Cambridge University Press, 1987.
Kaku, M., Quantum Field Theory: A Modern Introduction, Oxford University Press, 1993.
Weinberg, S., The Quantum Theory of Fields, Vol. II: Modern Applications, Cambridge University Press, 1996.
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Old October 12th, 2015, 10:24 AM
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Default Re: IISC Syllabus of Integrated Ph.D course (Physics)

Sir I am preparing for admission in IISC for Integrated Ph.D course so can you please provide me the syllabus for preparation
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Old October 12th, 2015, 10:26 AM
Super Moderator
 
Join Date: Nov 2011
Default Re: IISC Syllabus of Integrated Ph.D course (Physics)

Here I am providing you the syllabus.

SYLLABUS
Mechanics
Newtonian mechanics of a system of particles. Conservation of energy and momentum, collisions, simple harmonic motion, static equilibrium of a rigid body, rotational dynamics, angular momentum, gravitation, Kepler’s laws.
Properties of Matter
Stress and strain, elastic properties of solids, elastic modulii; Hydrostatics, elements of fluid mechanics, surface, tension and viscosity.

Wave Motion
Wave propagation, phase and group velocities, standing waves, Fourier analysis, sound as elastic waves, interference and diffraction of sound waves, Doppler effect.

Thermal Physics
Kinetic theory of gases, the Maxwell-Boltzmann distribution, thermal properties of ideal and real gases, liquids and solids, laws of thermodynamics, entropy, reversible and irreversible processes, Carnot cycle, heat engines, changes of phase, blackbody radiation, the Stefan-Boltzmann law. Planck’s law.

Electromagnetism, Electronics and Optics
Electric field and potential, Gauss law, Laplace and Poisson equations, electrostatic equilibrium, capacitance, dielectrics, electrostatic energy:
The magnetic field, magnetic forces on moving changes and current carrying wires, the Biot-Savart law, electromagnetic induction and Faraday’s law, magnetic susceptibility and permeability, direct and alternating current circuits, Maxwell’s equations, electromagnetic waves;
Semiconductors junctions, principles of rectification and amplification.
Reflection, refraction and polarisation of light, ray optics, thin lenses, aberrations, interference and diffraction of light, optical instruments.
Modern Physics Frames of reference, time dilation and length contraction, simultaneity, the Lorentz transformation, relativistic energy and momentum, mass-energy relation;

The photoelectric effect, the Compton effect, atomic spectra, wave-particle dualism, the wave function and its interpretation, the uncertainty principle, the Schrodingor equation.

Atomic structure, the Pauli exclusion principle, periodic classification of elements, spin of electrons, the Zeeman effect; generation and diffraction of x-rays, radioactivity, nucleus-constituents, binding, nuclear reactions, fission and fusion, nuclear reactors, particle accelerators, cosmic rays.
Experiments and Measurements

Errors in measurement, accuracy, measurements of length, mass and charge of small and large objects, fundamental constants. Basic knowledge of scientific instruments and their working.

Mathematical Physics
Theory of Systems of linear Equation. Linear algebra and matrices. Series and their convergence.
Limits and continuity, differentiation and integration, Taylor’s expansion, L’Hospital rule, maxima, minima. Analytical geometry of curves and surfaces. Ordinary (first and second order) differential equations. Complex numbers, roots of complex numbers, trigonometric identities, Argand’s diagram. Vector addition and products, gradient, divergence and curl, Gauss and Stokes theorems. Probability, basic laws of probability, mean, standard deviation.

MATHEMATICAL SCIENCES

SYLLABUS
1. Algebra
Theory of Equations Relations between roots and Coefficients. Newton’s identities. Rolle’s theorem, Reciprocal Equations, Des Cartes, Rule of Signs, Cubic and quark equations, Complex numbers and De Moivre’s Theorem. Determinants Cofactors, Properties of determinants, Solution of a Linear System, Cramer’s Rule. Inequalities AM-GM inequality, Cauchy-Schwarz inequality. Set Theory : Relations, Functions, Cardinality. Algebraic Structures Binary Operations, Groups, Rings: Definitions, Examples and Elementary Theorems. Vector Spaces Subspaces, Linear Independence, Bases, Dimension Linear Transformations, Matrices, Rank Nullity, Eigen values and Eigen vectors.

2. Geometry :
Two-dimensional Coordinate Geometry
Conics and their equations in Cartesian and Polar Coordinates, Ellipse, Parabola and Hyperbola.

Three-dimensional Co-ordinate Geometry
Planes, Lines, Spheres and Cones.
3. Vector Algebra and Vector Calculus : Vectors, addition, Scalar multiplication. Dot Product, Cross Product, Triple Product, Equations to the Line and the Plane. Grad, Divergence and Curl, Vector Integration, Green’s Gauss’ and Stokes’ Theorems.
4. Calculus and Analysis

Real Number System, Sequence and Series. Continuity, Differentiability. Mean Value Theorems, Indeterminate Value Theorem, L’Hospital Rule, Tangents and Normals, Maxima and Minima. Riemann Integration, Multiple Integrals, Partial differentiations, Lengths, areas and volumes by integration.
5. Differential Equations

First Order ODE Method of Separation of Variables: Exact equations: Euler’s equation: Orthogonal Family of curves, Second Order Linear ODE : Variation of Parameters.
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