Section 1: Mathematical Physics
Vector calculus: Linear vector spaces: 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 theorem, singular points, residue theorem and applications; Laplace transform, Fourier analysis; Physics Basic concepts of tensors: covariant tensors and contravariant tensors.
Section 2: Classical Mechanics
Lagrange’s formula: D’Alembert’s principle, Euler-Lagrange equation, Hamilton’s principle, c alculusof variations; Symmetry and conservation laws; Central force motion: Kepler’s problem and Rutherford scattering; Small oscillations: Coupled oscillations and normal modes; Rigid body dynamics: inertia tensor, orthogonal transformation, Euler angle, torque-free motion of symmetric top; Hamiltonian an dH amiltonian equation of motion; Liouville’s theorem; Gauge transformation: action angle Variables, Poisson brackets, Hamilton-Jacobi equation.
Lorentz transformation, relativistic kinematics, and mass-energy equivalence are elements of the special theory of relativity.
Section 3: Electromagnetic Theory
Solutions to electrostatic and magnetostatic problems involving boundary value problems; Image methods; Separation of variables; Dielectrics and conductors; Magnetic materials; Multipole expansion; Maxwell’s equations; Scalar and vector potentials; Coulomb and Lorentz meters; Free Electromagnetic waves in space, non-conducting and conducting media. The reflection as well as transmission at normal and oblique incidence will be discussed. Polarization of electromagnetic waves; Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves .
Section 4: Quantum Mechanics
Postulates of quantum mechanics – Uncertainty principle – Schrödinger equation – Dirac Bra-Ket representation -linear vectors-operators-Hilbert space-One-dimensional potential-step potential-finite rectangular well-barrier tunnel-particles in boxes-resonators-two-and three-dimensional systems-degeneracy-hydrogen atoms-angular momentum-spin-adding angular momentum-variational methods-WKB approximation-time-independent perturbation theory-basic scattering theory-Born approximation-symmetry in quantum mechanical systems.
Section 5: Thermodynamics and Statistical Physics
Laws of thermodynamics-Macroscopic microscopic states-phase space-Ensemble-Calculation partition functions-free energy-thermodynamic quantities-Classical quantum statistics-Degenerate Fermi gases-Blackbody radiation Planck’s distribution law-Bose-Einstein condensation-first second order phase transitions phase equilibria critical points.
Section 6: Atomic Molecular Physics
Spectra single multi-electron atoms-spin-orbit interactions LS jj coupling-fine hyperfine structures-Zeeman Stark effects-electric dipole transitions selection rules-rotational vibrational spectra diatomic molecules -Electronic transitions diatomic molecules Frank-Condon principle-Raman effect-EPR NMR ESR X-ray spectroscopy-Laser Einstein coefficient particle number inversion two three-level systems.
Section 7: Solid State Physics
Elements of crystallography-Diffraction methods structure determination-Adhesion in solids-Lattice vibrations thermal properties of solids-Free electron theory-Band theory solids-nearly free electron tight binding models-Metals, semiconductors insulators-Conductivity mobility effective mass-Optical properties solids-Kramer’s-Kronig relation-intra-band inter-band conversion-Dielectric properties solids-Dielectric function polarizability ferroelectricity-Magnetism solids-dia para ferro antiferro ferri Magnetism magnetic domains magnetic anisotropy-Superconductivity-Type I Type II superconductors Meissner effect London equation BCS theory flux quantization.
Section 8: Electronic Products
Balanced semiconductors – Statistics electrons holes intrinsic extrinsic semiconductors -Metal-semiconductor junctions-Ohmic rectifying contacts-PN diodes bipolar junction transistors field effect transistors-Negative positive feedback Basic knowledge circuits oscillators operational amplifiers active filters digital logic circuits combinational sequential circuits flip-flops timers counters scratchpads A/D D/A conversion.
Section 9: Nuclear Particle Physics
Nuclear radius charge distribution nuclear binding energy electric moment magnetic moment Semi-empirical quality formula-Nuclear model droplet model core-shell model-Nuclear force dinuclear problem-α decay β decay electromagnetic transition nucleus -Rutherford scattering nuclear reactions conservation laws-Fission fusion Particle accelerators detectors-Elementary particles photons baryons mesons leptons Quark model-Conservation laws isospin symmetry charge conjugation parity time reversal invariance.
