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Whatsapp no.**9454773728**

Mathematical :

basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: CauchyRiemann 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.

basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: CauchyRiemann 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.

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.

**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.

**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

Thermodynamics and Statistical

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.

**Atomic and Molecular :** 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.

**Solid State & 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.

**Nuclear and Particle : **