Download CLASSICAL MECHANICS I Space and Time – Newton`s Laws

CLASSICAL MECHANICS I
Space and Time – Newton’s Laws – Conservation Laws – Harmonic, Damped,
Forced, and Kicked Oscillators – Rocket Motion – Collision Problems – Projectiles – Central Forces – Inverse Square Law – Rutherford Scattering – Centrifugal
and Coriolis Forces – Potential Theory.
Principle of Least Action – Constraints and Generalised Coordinates – Lagrange’s Equations – Noether’s Theorem and Symmetries – Applications –
Hamilton’s Equations – Small Oscillations – Stability – Normal Modes.
Lorentz Transformations – Space-Time Diagrams – Length Contraction,
Time Dilation – Kinematics and Dynamics of a Particle – Composition of Velocities - Proper Time – Equations of Motion in Absolute Form and Relative
Form.
References:
1. Mechanics: Berkeley Physics Course, Vol. 1, by C. Kittel, W. D. Knight,
M. A. Ruderman, C. A. Helmholz, and B. J. Moyer; Tata-McGraw Hill.
2. Classical Mechanics, T.W.B. Kibble, F. H. Berkshire, World Scientific.
3. Principle of Mechanics by J. L. Synge and B. A. Griffith, Nabu Press,
2011.
CLASSICAL MECHANICS II
Review of Hamilton’s theory – Liouville’s theorem – Poincare Recurrence
Theorem – Poisson’s Brackets – Canonical Transformations – Action-Angle Variables – Adiabatic Invariants – Hamilton-Jacobi Theory.
Phase Space and Phase Portraits – First and Second Order Systems –
Predator-Prey Problems – Limit Cycles – Sensitivity to Initial Conditions and
Predictability – Integrability – Some Hamiltonian Systems which Exhibit Chaos
– Near Integrable Systems.
General Mathematical Formulation of Kinematics and Dynamics of Continuum Systems – Eulerian and Lagrangian Descriptions – Rigid Body Dynamics:
Angular Velocity – The Inertia Tensor – Angular Momentum – The Equations of
Motion – Eulerian Angles – Euler’s Equations – Elasticity: The Strain Tensor –
The Stress Tensor – Hooke’s Law – Homogeneous and Temperature-dependent
Deformations – Elastic Waves – Thermal Conduction and Viscosity – Fluid
Dynamics: Conservation Laws – Ideal Fluids – Viscous Fluids – Basics of Turbulence – Thermal Conduction and Diffusion in Fluids.
References:
1. Classical Mechanics, T.W.B. Kibble, F. H. Berkshire, World Scientific.
2. Elasticity: Course of Theoretical Physics, Vol. 7 by L.D. Landau and
E.M. Lifshitz; Butterworth Heinemann.
3. Fluid Mechanics: Course of Theoretical Physics, Vol. 6 by L.D. Landau
and E.M. Lifshitz; Butterworth Heinemann.
ELECTRODYNAMICS
Gradient, Divergence, Curl – Theorems of Gauss, Green, and Stokes.
Electrostatics: Charges, Fields, Potentials, Capacitance – Magnetostatics:
Currents, Fields, Potentials, Inductance – Electromagnetic Induction: Faraday’s
Law – Displacement Current.
Currents and Conductors: Uniqueness Theorems – Method of Images –
Ohms’ Law – Microscopic Theory of Conduction – Hall Effect.
Electric and Magnetic Fields in Matter: Polarization – Displacement – Magnetization – Boundary Conditions at a Surface of Discountinuity.
Conservation Laws: Conservation of of Energy – Poynting’s Theorem – Conservation of Momentum and Angular Momentum – Maxwell’s Stress Tensor.
References:
1. Electricity and Magnetism: Berkeley Physics Course, Vol. 2, by E. M.
Purcell; Tata-McGraw Hill.
2. Introduction to Electrodynamics: by D. J. Griffiths; Benjamin Cummings, Prentice-Hall of India.
3. Principles of Electrodynamics by Melvin Schwartz; Dover Publication.
OPTICS
Waves: Plane waves – Spherical Waves – Harmonic Waves – Phase Velocity – Wavepackets – Group Velocity – Plane Electromagnetic Waves: Linear,
Circular, and Elliptic Polarizations – Stokes Parameters, Polarisers.
Eikonal Approximation – Ray and Matrix Optics – Fermat’s Principle – Optical Imaging – Aberrations: Chromatic, Spherical, Coma, Astigmatism, Distortion – Optical Instruments.
Wave Optics: Reflection and Refraction – Interference and Interferometers
– Multiple-beam Interference – Coherent and Incoherent Light – Elementary
Theory of Diffraction: Kirchoff’ theory – Fraunhofer and Fresnel Diffraction –
Elementary Dispersion Theory – Elementary Scattering Theory.
References:
1. Fundamentals of Optics by F. Jenkins and H. White, Mc-Graw Hill.
2. Principles of Optics: M. Born and E. Wolf; Cambridge University Press.
THERMAL PHYSICS
The laws of Thermodynamics – Thermodynamic Potentials – Applications
of Thermodynamics – Equation of State – Description of Phase Transitions –
Surface Effects in Condensation – Van der Waals Equation of State – Osmotic
Pressure.
Probability – General Definitions – One Random Variable – Some Important
Probability Distributions – Many Random Variables.
Binary Collisions – Boltzmann Transport Equation – Boltzmann’s H Theorem – Maxwell-Boltzmann Distribution – Most Probable Distribution – Transport Phenomena – Mean Free Path – Conservation Laws – The Zeroth and First
Order Approximations – Viscosity – The Navier-Stokes Equation, Examples in
Hydrodynamics.
References:
1. Statistical Physics: Berkeley Physics Course, Vol. 5, by F. Reif; TataMcGraw Hill.
2. Statistical Mechanics by Kerson Huang, Wiley Eastern.
3. Statistical Physics of Particles by Mehran Kardar, Cambridge University
Press.
QUANTUM MECHANICS I
Experimental Background – The Old Quantum Theory – Uncertainty and
Complementarity – Discussion of Measurement – The Schrodinger and Heisenberg Pictures and Equivalence – Development of the Wave Equation – Interpretation of the Wave Function – Wave Packets in Space and Time – Eigenfunctions
and Eigenvalues – Energy and Momentum Eigenfunctions – Expectation Values
– Two-level System – One-dimensional Square Well and Barrier Potential – Linear Harmonic Oscillator – The Hydrogen Atom – Collisions in Three Dimensions
– Scattering by a Coulomb Field.
References:
1. Quantum Physics: Berkeley Physics Course, Vol. 4, by E. H. Wichman;
Tata-McGraw Hill.
2. Quantum Mechanics by L. I. Schiff, McGraw Hill.
3. Quantum Mechanics by E. Merzbacher, John Wiley.
STATISTICAL MECHANICS
General Definitions – The Microcanonical Ensemble – The Ideal Gas – Mixing Entropy and the Gibbs Paradox – The Canonical Ensemble – Examples –
The Grand Canonical Ensemble – The Equivalence of the Canonical and the
Grand Canonical Ensemble – Interacting Particles – The Cumulant Expansion
– The Cluster Expansion – Critical Point Behaviour.
The Postulates of Quantum Statistical Mechanics – Density Matrix – Ensembles in Quantum Statistical Mechanics – Ideal Gases: The Ideal Fermi Gas
– The Ideal Bose Gas – Applications – Statistical Mechanical Theory of Phase
Transitions: Ising Model.
References:
1. Statistical Mechanics by Kerson Huang, Wiley Eastern.
2. Statistical Physics of Particles by Mehran Kardar, Cambridge University
Press.
3. Statistical Physics: Course of Theoretical Physics, Vol. 5, Part 1, by L.D.
Landau and E.M. Lifshitz; Butterworth Heinemann.
QUANTUM MECHANICS II
Matrix Formulation of Quantum Mechanics: Bra and Ket Formulation –
Transformation Theory – Equations of Motion – Symmetry in Quantum Mechanics – Space and Time Displacements – Rotation – Angular Momentum
and Unitary Groups – Combination of Angular Momentum States and Tensor
Operators – Space Inversion and Time Reversal – Dynamical Symmetry.
Approximation Methods for Bound States: Stationary Perturbation Theory
– Variational Method – Dalgarno-Lewis Method – WKB Approximation – Timedependent Perturbation Theory.
Approximation Methods in Collision Theory: The Scattering Matrix – Stationary Collision Theory – Born Approximation – Distorted Wave Born Approximation – Partial Wave Analysis.
Identical Particles and Spin: Stern-Gerlach Experiment – Pauli Matrices –
Boson and Fermion Wavefunctions – Density Operator and Density Matrix.
References:
1. Quantum Mechanics by L. I. Schiff, McGraw Hill.
2. Quantum Mechanics by E. Merzbacher, John Wiley.
3. Quantum Mechanics: Course of Theoretical Physics, Vol. 3 by L.D. Landau and E.M. Lifshitz; Butterworth Heinemann.
CLASSICAL FIELD THEORY
Special Theory of Relativity: Experimental Basis – Lorentz Transformations
– Basic Kinematic Results – Addition of Velocities – 4-Velocity – Relativistic
Momentum and Energy of a Particle – Covariant formulation of Electrodynamics
– Transformation of Electromagnetic Fields – Solution of the Wave Equation
Covariant Form.
Classical Radiation Theory: Radiation by Moving Charges – Lienard-Wiechert
Potentials – Radiation from Relativistic Acceleration – Larmor Formula as Nonrelativistic Limit.
General theory of Relativity: The Principles of Equivalence – Local Lorentz
Invariance – General Coordinate Invariance – Geometry of Curved Spacetime.
Tensor Analysis: Parallel Displacement – Christoffel Symbols – Geodesics
– Covariant Differentiation – The Curvature Tensor – The Bianchi Relations –
The Ricci Tensor – Einstein’s Field Equations – The Schwarzschild Solution.
Experimental Tests: The Gravitational Redshift, Deflection of Light by the
Sun, Precession of Perihelia of Mercury.
References:
1. The Classical Theory of Fields: Course of Theoretical Physics, Vol. 2 by
L.D. Landau and E.M. Lifshitz; Butterworth Heinemann.
2. A first course in General Relativity, Bernard F Schutz, Cambridge University Press.
3. Relativity (Special, General and Cosmological) by W. Rindler, Oxford
university Press.
ADVANCED QUANTUM MECHANICS
Nonrelativistic Quantum Mechanics: Selection rules for dipole transitions
in hydrogen – Spontaneous and stimulated emission, absorption – Lifetime of
excited states – Line shape and width – Fine structure of hydrogen – Path
Integrals – Aharonov Bohm Effect – Geometric Phase – Coherent States.
Relativistic Quantum Mechanics: Klein Gordon Equation – Dirac Equation
– Canonical (second) quantization of a wave field – Quantization of the free
Maxwell field.
References:
1. Quantum Mechanics by L. I. Schiff, Mc-Graw Hill.
2. Quantum Field Theory by F. Mandl and G. Shaw., Wiley.
CONDENSED MATTER PHYSICS
Non-Equilibrium Statistical Mechanics: Systems Close to Equilibrium – Onsager’s Regression Hypothesis and Time Correlation Functions – Application
to Chemical Kinetics – Application to Self-Diffusion – Fluctuation-Dissipation
Theorem – Response Functions – Absorptions – Friction and Langevin Equation
– Fokker-Planck Equations – Master Equations – Quantum Dynamics – Linear
Response Theory.
Condensed Matter Physics: Crystal Structure – Wave Diffraction and Reciprocal Lattice – Crystal Binding and Elastic Constants – Crystal Vibrations:
Phonons – Thermal Properties – Free Electron Fermi Gas – Energy Bands –
Semiconductor Crystals – Fermi Surfaces and Metals – Superfluidity and Superconductivity – Diamagnetism and Paramagnetism – Ferromagnetism and
Antiferromagnetism – Magnetic Resonance – Dielectrics and Ferroelectrics –
Point Defects – Dislocations.
References:
1. Non-Equilibrium Statistical Mechanics by Robert Zwanzig, Oxford University Press.
2. Statistical Physics II: Nonequilibrium Statistical Mechanics by R. Kubo,
M. Toda, N. Hashitsume, Springer.
3. Introduction to Solid State Physics by C. Kittel, Wiley.
4. Solid State Physics by N. W. Ashcroft and N. D. Mermin, Brooks Cole.
STRUCTURE OF MATTER
Atomic Physics: Review of Hydrogen Atom – Pauli Exclusion Principle and
Helium Atom – Many-Electron Systems – Dipole transitions (selection rules) –
Photoelectric Effect.
Molecular Physics: Born- Oppenheimer Approximation – Hydrogen Molecule
– Concept of Valence – Vibrational and Rotational Levels - Selection Rules –
Raman effect.
Nuclear Physics: Basic Nuclear Properties (Mass, Radius, Isotopes) – Mass
Formula – Deuteron Problem (Scattering Length, Effective Radius) – Shell
Model – Liquid Drop Model – Radioactivity – Parity Violation in Beta Decay – Detectors and Accelerators.
Particle Physics: Properties of Elementary Particles – Conservation Laws
– Quark Model – Strong Interactions – pi-N Scattering (Including Isospin) –
Electromagnetic Interaction- Magnetic Moments of the Baryon Octet – Weak
Interactions – Parity and Charge Conjugation Violation – Neutrino Oscillations
– CP-Violation.
References:
1. Physics of Atoms and Molecules by B. H. Bransden and C. J. Joachain,
Pearson Education.
2. Introduction to Nuclear Physics, K.S. Krane, Wiley 1987.
3. Quarks and Leptons: Introductory Course in Modern Particle Physics,
Francis Halzen, Alan D. Martin, Wiley 1984.