Relativity & Statistical Physics

SYLLABUS- RELATIVITY & STATISTICAL PHYSICS, Unit-I
Relativity: Reference systems, inertial frames, Galilean invariance and conservation laws,
propagation of light, Michelson-Morley experiment; search for ether.
Postulates for the special theory of relativity, Lorentz transformations, length contraction,
time dilation, velocity addition theorem, variation of mass with velocity, mass-energy
equivalence, particle with a zero rest mass.
Unit-II
Statistical physics: The statistical basis of thermodynamics: Probability and
thermodynamic probability, principle of equal a prior probabilities, probability
distribution and its narrowing with increase in number of particles. The expressions for
average properties. Constraints; accessible and inaccessible states, distribution of particles
with a given total energy into a discrete set of energy states.
Unit-III
Some universal laws: The ji- space representation, division of i-space into energy sheets
and into phase cells of arbitrary size, applications to one-dimensional harmonic oscillator
and free particles. Equilibrium before two systems in thermal contact, bridge with
macroscopic physics. Probability and entropy, Boltzmann entropy relation. Statistical
interpretation of second law of thermodynamics. Boltzmann canonical distribution law
and its applications; rigorous form of equipartition of energy.
Unit-IV
Maxwellian distribution of 0 speeds in an ideal gas: Distribution of speeds and of
velocities, experimental verification, distinction between mean, r.m.s. and most probable
speed values. Doppler broadening of spectral lines.
Transition to quantum statistics: 'h' as a natural constant and its implications, cases of
particle in a one-dimensional box and one-dimensional harmonic oscillator,
Indistinguishability of particles and its consequences, Bose-Einstein, and Fermi-Dirac
distributions, photons in black body chamber, free electrons in a metal, Fermi level and
Fermi energy.