Statistical Mechanics

Overview

Instructor: Prof. Ashwin Joy, Department of Physics, IIT Madras.

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

Syllabus

Lecture 01-Discrete Probability.
Lecture 02-Continous Probability.
Lecture 03 Characteristic Function.
Lecture 04-Gausssian Distribution.
Lecture 05-Binomial Distribution.
Lecture 06-Poisson Distribution.
Lecture 07-Central Limit Theorem.
Lecture 08-Many Random Variables.
Lecture 09-Entropy and Probability.
Lecture 10-Entropy Maximization.
Lecture 11-Transformation of Random Variable.
Lecture 12-Tutorial.
Lecture 13-Mathematical Preliminaries 1.
Lecture 14-Microcanonical Ensemble.
Lecture 15-Two Level System (Microcanonical Ensemble).
Lecture 16-Classical Ideal Gas (Microcanonical Ensemble).
Lecture 17-Entropy of Mixing.
Lecture 18-Classical Ideal Gas (Canonical Ensemble).
Lecture 19-Gibbs Canonical Ensemble.
Lecture 20-Canonical Ensemble.
Lecture 21-Classical Ideal Gas (Gibbs Canonical Ensemble).
Lecture 22-Two Level System (Canonical Ensemble).
Lecture 23-N Spins in a Uniform Magnetic Field.
Lecture 24-Grand Canonical Ensemble.
Lecture 25-Ideal Gas (Grand Canonical Ensemble).
Lecture 26-N Non - Interacting Spins in Constant Magnetic Field.
Lecture 27-Quantum statistical mechanics.
Lecture 28-Statistics of Fermions and Bosons.
Lecture 29-Quantum to Classical Correspondance.
Lecture 30-Vibrations of Solid (Low Temperature).
Lecture 31-Vibrations of Solid (Continuation).
Lecture 32 Free Electrons(Fermi Gas) in a Metal.
Lecture 33 Free Electrons(Fermi Gas) in a Metal(Continuation).
Lecture 34 - Problem solving demo - part 1.
Lecture 35 - Problem solving demo - part 2.