Physics 7225
Statistical Mechanics
Spring 2023
J. A. Sauls

Lectures Notes

  • 1/17/2023: Lecture 1 - Brownian Motion, Random Walk and Diffusion [PDF]
  • 1/17/2023: Useful properties of the Gamma Function [PDF]
  • 1/19/2023: Lecture 2 - Langevin's Theory of Brownian Motion [PDF]
  • 1/24/2023: Lecture 3 - Maxwell-Boltzmann Distributions - Part I [PDF]
  • 1/31/2023: Lecture 4 - Maxwell-Boltzmann Distributions - Part II [PDF]
  • 2/07/2023: Lecture 5 - Gibbs Distribution - Part I [PDF]
  • 2/09/2023: Lecture 6 - Gibbs Part II - Black-Body Radiation [PDF]
  • 2/14/2023: Lecture 7 - Bose-Einstein Gases I - Grand Partition Function [PDF]
  • 2/16/2023: Lecture 8 - Bose-Einstein Gases II - Bose-Einstein Condensation [PDF]
  • 2/23/2023: Lecture 9 - Bose-Einstein Gases III - Thermodynamics [PDF]
  • 2/28/2023: Notes on Indistinguishability of Identical Particles in Quantum Mechanics [PDF]
  • 2/28/2023: Lecture 10 - Fermi-Dirac Statistics & Many Fermion Ground State [PDF]
  • 3/02/2023: Lecture 11 - Fermi-Dirac Gases II - Statistical Mechanics [PDF]
  • 3/07/2023: Lecture 12 - Fermi-Dirac Gases III - Thermal Excitations, Heat Capacity of Metals [PDF]
  • 3/09/2023: Lecture 13 - Fermi-Dirac Gases IV - Sommerfeld Expansion, Entropy & Heat Capacity [PDF]
  • 3/21/2023: Lecture 14 - Fermi-Dirac Gases V - Equation of State [PDF]
  • 3/23/2023: Lecture 15 - Paramagnetism [PDF]
  • 3/30/2023: Lecture 16 - Relativistic Fermi Systems [PDF]
  • 4/06/2023: Lecture 17 - Phase Transitions & Correlation Functions - Heisenberg Model [PDF]
  • 4/06/2023: Broken Symmetry Phase Transitions & and Order Parameters: Some Examples [PDF]
  • 4/11/2023: Lecture 18 - Bose-Einstein Gas: 1-particle Density matrix & Long-Range Order [PDF]
  • 4/13/2023: Lecture 19 - Bose-Einstein Condensates as Coherent States of a Quantum Field [PDF]
  • 4/18/2023: Lecture 20 - Dilute Interacting BE Gases - Gross-Pitaevskii Theory [PDF]
  • 4/20/2023: Lecture 21 - Special Solutions to the Gross-Pitaevskii Equations [PDF]
  • 4/25/2023: Lecture 22 - Phase Quantization, Persistent Currents & Superfluidity [PDF]
  • 4/27/2023: Lecture 23 - Phase Transitions I - Landau Theory - Ferromagnetism [PDF]
  • 5/02/2023: Lecture 24 - Phase Transitions II - Landau Critical Exponents [PDF]
  • 5/04/2023: Lecture 25 - Phase Transitions III - Superconductivity, Meissner Effect & Flux Quantization [PDF]

    • References and Textbooks

  • Notes on Gaussian Integrals [PDF]
  • Atomic Quantum Gases - Ketterle's Group at MIT
  • Abramowitz and Stegun: Handbook of Mathematical Functions [online]
  • Stochastic Problems in Physics and Astronomy, S. Chandrasekhar, [ Reviews of Modern Physics, 15, 1 (1943) ]
  • Statistical Mechanics by Pathria and Beale [Chapters]
  • Statistical Mechanics by Pathria and Beale - Single File [PDF]