and to successfully administer and manage the activities as Faculty in the Interactive Curriculum of a progressive and vibrant Academic Institutions.
Section 1: Mathematical Physics Vector calculus:
linear vector space: basis, orthogonality and completeness; matrices; similarity transformations, diagonalization, eigenvalues and eigenvectors; linear differential equations:
second order linear differential equations and solutions involving special functions; complex analysis: Cauchy Riemann conditions, Cauchy's theorem, singularities, residue theorem and
applications; Laplace transform, Fourier analysis; elementary ideas about tensors: covariant and contravariant tensors
Section 2: Classical Mechanics Lagrangian formulation: D'Alembert's principle, Euler Lagrange equation, Hamilton's principle, calculus of variations; symmetry and conservation laws; central force motion: Kepler problem
and Rutherford scattering; small oscillations: coupled oscillations and normal modes; rigid body dynamics: interia tensor, orthogonal transformations, Euler angles, Torque free motion of a symmetric top; Hamiltonian and Hamilton's equations of motion; Liouville's theorem; canonical transformations: action angle variables, Poisson brackets, Hamilton Jacobi equation.
Special theory of relativity: Lorentz transformations, relativistic kinematics, mass-energy equivalence
Section 3: Electromagnetic Theory Solutions of electrostatic and magnetostatic problems including boundary value problems; method of images; separation of variables; dielectrics and conductors; magnetic materials;
multipole expansion; Maxwell's equations; scalar and vector potentials; Coulomb and Lorentz gauges; electromagnetic waves in free space, non-conducting and conducting media; reflection
and transmission at normal and oblique incidences; polarization of electromagnetic waves; Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge
Section 4: Quantum Mechanics Postulates of quantum mechanics; uncertainty principle; Schrodinger equation; Dirac BraKet notation, linear vectors and operators in Hilbert space; one dimensional potentials: step
potential, finite rectangular well, tunneling from a potential barrier, particle in a box, harmonic oscillator; two and three dimensional systems: concept of degeneracy; hydrogen atom; angular
momentum and spin; addition of angular momenta; variational method and WKB approximation, time independent perturbation theory; elementary scattering theory, Born approximation;
symmetries in quantum mechanical systems
Section 5: Thermodynamics and Statistical Physics Laws of thermodynamics; macrostates and microstates; phase space; ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics;
degenerate Fermi gas; black body radiation and Planck's distribution law; Bose-Einstein condensation; first and second order phase transitions, phase equilibria, critical point.
Section 6: Atomic and Molecular Physics Spectra of one-and many-electron atoms; spin-orbit interaction: LS and jj couplings; fine and hyperfine structures; Zeeman and Stark effects; electric dipole transitions and selection rules;
rotational and vibrational spectra of diatomic molecules; electronic transitions in diatomic molecules, Franck-Condon principle; Raman effect; EPR, NMR, ESR, X-ray spectra; lasers:
Einstein coefficients, population inversion, two and three level systems
Section 7: Solid State Physics Elements of crystallography; diffraction methods for structure determination; bonding in solids; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids:
nearly free electron and tight binding models; metals, semiconductors and insulators; conductivity, mobility and effective mass; Optical properties of solids; Kramer's-Kronig relation,
intra-and inter-band transitions; dielectric properties of solid; dielectric function, polarizability, ferroelectricity; magnetic properties of solids; dia, para, ferro, antiferro and ferri-magnetism,
domains and magnetic anisotropy; superconductivity: Type-I and Type II superconductors, Meissner effect, London equation, BCS Theory, flux quantization
Section 8: Electronics Semiconductors in equilibrium: electron and hole statistics in intrinsic and extrinsic semiconductors; metal-semiconductor junctions; Ohmic and rectifying contacts; PN diodes,
bipolar junction transistors, field effect transistors; negative and positive feedback circuits; oscillators, operational amplifiers, active filters; basics of digital logic circuits, combinational and
sequential circuits, flip-flops, timers, counters, registers, A/D and D/A conversion.
Section 9: Nuclear and Particle Physics Nuclear radii and charge distributions, nuclear binding energy, electric and magnetic moments; semi-empirical mass formula; nuclear models; liquid drop model, nuclear shell model; nuclear
force and two nucleon problem; alpha decay, beta-decay, electromagnetic transitions in nuclei Rutherford scattering, nuclear reactions, conservation laws; fission and fusion; particle
accelerators and detectors; elementary particles; photons, baryons, mesons and leptons; quark model; conservation laws, isospin symmetry, charge conjugation, parity and time-reversal
invariance
