Statistical mechanics : an advanced course with problems and solutions

1. Principles of Statistical Mechanics. Microscopic states. Statistical treatment. The principle of equal weight and the microcanonical ensemble. The thermodynamic weight of a macroscopic state and entropy. Number of states and the density of states. Normal systems in statistical thermodynamics. Contact between two systems. Quasi-static adiabatic process. Equilibrium between two systems in contact. Fundamental laws of thermodynamics. The most probable state and fluctuations. Canonical distributions. Generalized canonical distributions. Partition functions and thermodynamic functions. Fermi-, Bose-, and Boltzmann- statistics. Generalized entropy. 2. Applications of the Canonical Distribution. General properties of the partition function Z( ). Asymptotic evaluations for large systems. Asymptotic evaluations and legendre transformations of thermodynamic functions. Grand partition function . Partition functions for generalized canonical distributions. Classical configurational partition functions. Density matrices. 3. Statistical Thermodynamics of Gases. Partition functions of ideal gases. Internal degrees of freedom and internal partition functions. Mixtures of ideal gases. Molecular interactions. Cluster expansion. 4. Applications of Fermi- and Bose- Statistics. Fundamental formulae of Fermi-statistics. Fermi distribution function. Electronic energy bands in crystals. Holes. Semiconductors. Bose-statistics, liquid Helium. 5. Strongly Interacting Systems. Molecular field approximation. Bragg-Williams approximation. Cooperative phenomena. Average potential in charged particle systems. Debye-Huckel theory. Distribution functions in a particle system. 6. Fluctuations and Kinetic Theories. Fluctuations. Collision frequency. Boltzmann transport equation. Index.