The following list contains the topics that I will cover. These are taken from the B.Sc. Physics Honours syllabus (Statistical Mechanics, PHSACOR14T).
- System of identical particles: Collection of non-interacting identical particles. Classical approach and quantum approach: Distinguishability and indistinguishability. Occupation number and MB distribution, emergence of Boltzmann factor. Composite system postulate and symmetry postulate of quantum mechanics (for a pair of particles only). Bosons and fermions. Spin statistics theorem (statement only). Pauli’s exclusion principle.
- Bose-Einstein Statistics: B-E distribution law, Thermodynamic functions of a strongly degenerate Bose gas, Bose-Einstein condensation, properties of liquid He (qualitative description), Radiation as a photon gas and Thermodynamic functions of photon gas. Bose’s derivation of Planck’s law. Phonon gas. Debye theory of specific heat of solids. $T^3$ law.
- Fermi-Dirac Statistics: Fermi-Dirac distribution Law, Thermodynamic functions of a completely and strongly degenerate Fermi gas, Fermi energy, Fermi temperature, Fermi momentum, Sommerfield correction to the free electron theory for a metal. Specific heat of metals, Wiedemann-Franz law.