The course is designed to give the students a firm understanding of statistical mechanics at the advanced undergraduate/beginning graduate level. After a discussion of the concepts of probability, the postulates of classical mechanics are developed in various ensembles of physical relevance. The ideas thus developed for the classical systems will be shown to have serious limitations when applied to quantum systems. Finally, we develop the correct theory of statistical mechanics for quantum systems and show that classical results can be recovered from the quantum theories in the high temperature - low density limit.
Week 1 : Random Variables
Week 2 : Moments & Cumulants
Week 3 : Important Probability Distributions
Week 4 : Maximum Entropy Principle.
Week 5 : Micro-canonical Ensemble
Week 6 : Canonical Ensemble
Week 7 : Gibbs Canonical Ensemble
Week 8 : Grand Canonical Ensemble
Week 9 : Ideal Gas of Mass-less Particles (Photons & Phonons)
Week 10 : Ideal Gas of Real Particles (Fermions & Bosons)
Week 11 : Electrons in Metals
Week 12 : Classical Limit of Quantum Gases