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Course

JEST Syllabus

Mathematical Methods

Vector algebra and vector calculus; linear vector spaces, linear operators, matrices and Eigenvalue problem; Sturm Liouville theory, classical orthogonal polynomials; linear ordinary differential equations, exact and series methods of solution ; linear partial differential equations, solution by separation of variables; complex variables, analytic functions,Taylor and Laurent expansions, contour integration; Fourier and Laplace transforms.

Classical Mechanics

Newtons laws, conservation of energy and momentum, collisions; generalized coordinates,principle of least action, Lagrangian and Hamiltonian formulations of mechanics;  symmetry and conservation laws; central force problem, Kepler problem; rigid body motion; small oscillations and normal modes; special relativity in classical mechanics.

Electromagnetic Theory

Laws of electrostatics and magneto statics, methods of solving boundary value problems,multipole expansion; fields in conducting, dielectric, diamagnetic and paramagnetic materials; Faradays law and time varying fields; conservation

of charge, displacement current;  Max wells  equations;  energy  and  momentum  of  electromagnetic  fields,  Poynting theorem; propagation of plane electromagnetic waves, reflection and refraction of planeel ectromagnetic waves, electromagnetic waves in dispersive and conducting media; scalar

and vector potentials,  Coulomb and Lorentz gauge,  wave equation in terms of electromagnetic potentials; radiation from moving charges, retarded and advanced potentials,Lienard-Wiechert potentials, multipole radiation, Larmors formula.

Quantum Mechanics

The  uncertainty  principle;  conceptual  basis  of  quantum  mechanics;  Schrodinger  equation, problems in one, two and three dimensions, bound states and tunnelling, particle in  a  box,  harmonic  oscillator,  hydrogen  atom;  matrix  formulation  of  quantum  theory, unitary transformations and Hermitian operators and their properties; orbital and spin angular momenta, addition of angular momenta; time independent and time dependent perturbation theory, Fermi golden rule; elementary scatte

ring theory.

Thermodynamics and Statistical Physics

Laws of thermodynamics; work and heat; thermodynamic potentials, Maxwells relations; statistical ensembles; partition function; classical ideal gas, harmonic oscillators; classical and  quantum  statistics;  Fermi  and  Bose  gases;  black  body  radiation;  first  and  second order phase transitions.

Solid State Physics

Simple crystal structures and X-ray diffraction;  lattice vibrations and thermal properties  of  solids;  free  electron  theory;  band  theory  of  solids; metals,  semiconductors  and insulators; basic electrical, optical and magnetic properties of solids; elements of super- conductivity.  Electronics Diodes, rectifier circuits, junctions, transistors and field effect devices; device characteristics, frequency dependence and applications like active filters and oscillator circuits; solar cells, photo detectors, and

LEDS; operational amplifiers and their applications; Boolean algebra, digital techniques and applications:  registers, couters,  comparators  and  similar  circuits;  A/D  and  D/A  converters;  microprocessor  andmicrocontroller basics.

Nuclear and Particle Physics

Structure of the nucleus;  binding energy,  nuclear fusion and fission;  radioactive decay, barrier penetration by alpha particles; classification of elementary particles and fundamental interactions, leptons and hadrons, elementary ideas of quark model; conservation laws in particle reactions. Atomic and Optical Physics Interference,  diffraction and polarization of light;  photo

electric effect;  spectra of single and  multiple  electron  atoms;  Zeeman  and  Stark  effects;  electric  dipole  transition  and selection rules; hyperfine structure; spontaneous and stimulated emission. Experimental data and error analysis Probability theory Gaussian  and  Poisson  distributions;  error  analysis;  propagation  of  errors;  significant figures; least square fitting.

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