Statistical Mechanics: An Advanced Course with Problems and Solutions

approximation assumed atoms average Boltzmann Boltzmann equation calculate CALIFORNIA/SANTA CRUZ canonical distribution chemical potential classical coefficient collision condition conduction band constant coordinates cosh CRUZ The University defined degeneracy denoted density matrix derived distribution function donor level E₁ electric electrons entropy equal equation Fermi filled band formula given Hamiltonian heat capacity Helmholtz free energy Hence ideal gas integral interaction kinetic kT log microscopic molecular field molecules momentum motion N₁ N₂ NOTE number density number of particles obtains oscillator partition function phase space probability problem quantum mechanics r₁ relation rotational partition function sinh solution to example specific heat spin statistical mechanics Stirling's formula term theorem thermodynamic total number UNIVERSITY OF CALIFORNIA/SANTA velocity vibration volume zero μο ат др дх