0. Review (Thermodynamics, Quantum Mechanics, Classical Mechanics, Math)
I. Fundamentals of equilibrium statistical mechanics (postulates, ensemble, probability distribution)
II. Ensembles
II.1 Microcanonical ensemble, partition function, and thermodynamic properties
II.2 Canonical ensemble, partition function, and thermodynamic properties
II.3 Grand canonical ensemble, partition function, and thermodynamic properties
III. Statistics
III.1 Independence
III.2 Distinguishable, indistinguishable particles
III.3 Boltzmann statistics
III.4 Fermi-Dirac and Bose-Einstein statistics
IV. “Perfect Boltzmann” gas
V. Atoms and molecules in the classical limit (Boltzmann statistics) and thermodynamic properties
V.1 Atoms
V.2 Molecules
VI. Chemical equilibrium
VI.1 Energy zero
VI.2 Equilibrium constant
Examples
VII. Ideal Fermi-Dirac gas
VII.1 Weakly degenerate FD gas
VII.2 Strongly degenerate FD gas - Conduction electrons in metals
VIII. Ideal Bose-Einstein gas
VIII.1 Weakly degenerate BE gas
VIII.2 Strongly degenerate BE gas – Bose Einstein Condensation
VIII.3 Photon gas
VIII.4 Phonon gas
IX. Classical statistical mechanics
IX.1 Phase space and classical mechanical partition function
IX.2 Gas of structureless particles
X. Classical statistical mechanics of fluids (imperfect gases and liquids)
X.1 Interaction potentials
X.2 Structural properties
XI. Analytical Methods and Computer Simulations
XI.1 Analytical methods
XI.2 Monte Carlo and Molecular Dynamics Methods
XI.3 Example: Phase Diagrams from Grand Canonical Monte Carlo calculations
XII. Time dependence