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PRINCIPLES OF STATISTICAL MECHANICS
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approximation assumed average Boltzmann Boltzmann equation calculate canonical distribution chemical potential coefficient collision condition conduction band considered constant coordinates corresponding cosh crystal defined degeneracy degrees of freedom denoted density matrix derived determined distribution function donor level energy levels entropy equal equation expression Fermi gas Fermi potential filled band frequency gas molecules given grand partition function Hamiltonian heat capacity Helmholtz free energy Hence high temperatures ideal gas integral interaction internal energy lattice low temperatures magnetic field mass mean microscopic molecular field molecules momentum motion Note number density number of particles obtains partition function phase space pressure probability quantum mechanics relation respectively rotational rotational partition function sinh solution to example specific heat spin statistical mechanics Stirling's formula sublattice Substituting summation term theorem theory thermal equilibrium total number transformation unit volume velocity vibration wave zero