Section 1: Mathematical Physics

Linear vector space: basis, orthogonality and completeness; matrices; vector

calculus; linear differential equations; elements of complex analysis: Cauchy-
Riemann conditions, Cauchy’s theorems, singularities, residue theorem and

applications; Laplace transforms, Fourier analysis; elementary ideas about tensors:

covariant and contravariant tensor, Levi-Civita and Christoffel symbols.

Section 2: Classical Mechanics

D’Alembert’s principle, cyclic coordinates, variational principle, Lagrange’s

equation of motion, central force and scattering problems, rigid body motion;

small oscillations, Hamilton’s formalisms; Poisson bracket; 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; dielectrics and conductors; Maxwell’s equations; scalar and vector

potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their

reflection, refraction, interference, diffraction and polarization; 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;

one-, two- and three-dimensional potential problems; particle in a box, transmission

through one dimensional potential barriers, harmonic oscillator, hydrogen atom;

linear vectors and operators in Hilbert space; angular momentum and spin;

addition of angular momenta; time independent perturbation theory; elementary

scattering theory.

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; LS and jj coupling; hyperfine structure;

Zeeman and Stark effects; electric dipole transitions and selection rules; rotational

and vibrational spectra of diatomic molecules; electronic transition in diatomic

molecules, Franck‐Condon principle; Raman effect; NMR, ESR, X-ray spectra;

lasers: Einstein coefficients, population inversion, two and three level systems.

Section 7: Solid State Physics & Electronics

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,

dielectric and magnetic properties of solids; elements of superconductivity: Type-I

and Type II superconductors, Meissner effect, London equation.

Semiconductor devices: diodes, Bipolar Junction Transistors, Field Effect Transistors;

operational amplifiers: negative feedback circuits, active filters and oscillators;

regulated power supplies; basic digital logic circuits, sequential circuits, flip‐flops,

counters, registers, A/D and D/A conversion.

Section 8: Nuclear and Particle Physics

Nuclear radii and charge distributions, nuclear binding energy, Electric and

magnetic moments; nuclear models, liquid drop model: semi‐empirical mass

formula, Fermi gas model of nucleus, 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.

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