Formulation of Statistical Methods: Specification of the state of a system, concept of ensembles, elementary probability calculations, distribution functions, statistical interpretation of entropy (Boltzmann theorem)

Statistical Ensembles: Microcanonical ensemble, canonical ensemble and examples (e.g., paramagnet), calculation of mean values, calculation of partition function and its relation with thermodynamic quantities, the grand canonical ensemble and examples (e.g. adsorption), calculation of partition function and thermodynamic quantities

Simple Applications of Ensemble Theory: Monoatomic ideal gas in classical and quantum limit, Gibb’s paradox and quantum mechanical enumeration of states, equipartition theorem and examples (ideal gas, harmonic oscillator), specific heat of solids, quantum mechanical calculation of paramagnetism

Quantum Statistics: Indistinguishibility and symmetry requirements, Maxwell-Boltzmann statistics, Bose-Einstein and photon statistics, Fermi-Dirac statistics (distribution functions, partition functions). Examples: polyatomic ideal gas (MB), black body radiation (photon statistics), conduction electrons in metals (FD), Bose condensation (BE).

Systems of Interacting Particles: Lattice vibrations in solids, van der Waals gas, mean field calculation, ferromagnets in mean field approximation

Recommended Text:
1. W. Brewer, F. Schwabl, “ Statistical Mechanics”, Springer Verlag (2002).
2. F.Reif, Fundamentals of Statistical and Thermal Physics McGraw Hill, (1965).
3. T. L. Hill, “ Statistical Mechanics”, World Scientific Publishing Company, (2004)
4. K. Huang, “Statistical Mechanics”, John Wiley and Sons (1988).