Statistical Mechanics

Accordingly approximation atoms behavior Bose gas Bose-Einstein bosons canonical ensemble chemical potential classical condition configuration constant coordinates corresponding d³r denotes density derive determined distribution function eigenvalues electron entropy equation equilibrium evaluate expansion expression factor Fermi gas fermions ferromagnet field fluctuations fluid formula free energy given system grand canonical ensemble grand partition function Hamiltonian helium hence ideal identically equal integral interparticle interactions lattice limit liquid magnetic matrix mean microstates molecules momentum motion N₁ number of particles obtain operator oscillator parameter phase transition phonons Phys physical system potential pressure problem pseudopotential quantity quantum quantum-mechanical result rotational single-particle specific heat spectrum spin statistics Substituting summation superfluid theorem theory thermal thermodynamic total number two-body variable velocity virial coefficient volume vortex vortex ring wave function whence it follows zero