Mathematical Physics covering Linear Vector Spaces, Matrices, Differential Equations, Special Functions, Complex Analysis, Integral Transforms, and Tensor Calculus

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 (inertia 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)

Electromagnetic Theory - Electrostatics and Magnetostatics, Maxwell's Equations, Wave Propagation, Boundary Interactions, Energy Transport, and Radiation Phenomena

Section 4: Quantum Mechanics - Postulates of quantum mechanics, uncertainty principle, Schrodinger equation, Dirac Bra Ket notation, linear vectors and operators in Hilbert space, one dimensional potentials (step potential, finite rectangular well, tunneling, particle in a box, harmonic oscillator), two and three dimensional systems with degeneracy, hydrogen atom, angular momentum and spin, addition of angular momenta, variational method, WKB approximation, time independent perturbation theory, elementary scattering theory, Born approximation, and 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 & 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 - Comprehensive coverage of crystallography, electronic structure, transport properties, optical, dielectric, magnetic properties, and superconductivity

Section 8: Electronics - Semiconductor Fundamentals, Metal-Semiconductor Junctions, Semiconductor Devices, Analog Circuits, Digital Electronics

Section 9: Nuclear 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