Net jrf physics

Physical Sciences

PAPER I - SECTION – B

1. Basic Mathematical Methods: Calculus:  Vector algebra and vector calculus. Linear algebra, matrices. Linear differential equations. Fourier – series, Elementary complex analysis.

2. Classical Dynamics: Basic principles of classical dynamics. Lagrangian and Hamiltonian formalisms. Symmetries and conservation laws. Motion in the central field of force. Collisions and scattering. Mechanics of a system of particles. Small oscillations and normal modes. Wave motion – wave equation, phase velocity, group velocity, dispersion. Special theory of relativity – Lorentz transformations, addition of velocities, mass – energy equivalence.

3. Electromagnetism: Electrostatics – Laplace and Poisson equations, boundary value problems. Magnetostatics – Ampere’s theorem, Biot – Savart Law, electromagnetic induction. Maxwell’s equations in free space and in linear isotropic media. Boundary conditions on the fields at interfaces. Scalar and vector potentials. Gauge invariance. Electromagnetic waves – reflection and refraction, dispersion, interference, coherence, diffraction, polarization. Electrodynamics of a charged particle in electric and magnetic fields. Radiation from moving charges, radiation from a dipole. Retarded potential.

4. Quantum Physics and Applications : Wave – particle duality. Heisenberg’s uncertainty Principle. The Schrodinger equation Particle in a box, Harmonic Oscillator, Tunnelling through a barrier. Motion in a central potential, Orbital angular momentum. Angular momentum algebra, spin. Addition of angular momenta. Time – independent perturbation theory. Fermi’s Golden Rule. Elementary theory of scattering in a central potential. Phase shifts, partial wave analysis, Born approximation, identical particles, spin – statistics connection.

5. Thermodynamic and Statistical Physics : Laws of thermodynamics and their consequences, Thermodynamic potentials and Maxwell’s relations. Chemical potential, phase equilibria. Phase space, microstates and macrostates. Partition function. Free Energy and connection with thermodynamic quantities. Classical and quantum statistics, Degenerate electron gas. Blackbody radiation and Planck’s distribution law, Bose-Einstein condensation. Einstein and Debye models for lattice specific heat.