Statistical Mechanics: An Advanced Course with Problems and Solutions

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