The Ideal Quantum Gas

Abstract

A quantum system of N identical particles is described by the wave function $$\Psi = \Psi ({q_1}, \ldots {q_N}),$$ (8.1) where q j denotes all compatible coordinates of particle j (position and spin, for example). However, not all wave functions of this sort, which satisfy the time-independent Schrödinger equation, are acceptable representations of a quantum system. We also require a symmetry property, $$\Psi ({q_1}, \ldots ,{q_i}, \ldots ,{q_j}, \ldots ,{q_N}) = \pm ({q_1}, \ldots ,{q_j}, \ldots ,{q_i}, \ldots ,{q_N}),$$ (8.2) which indicates that the quantum state of the system does not alter if we change the coordinates of two particles. The symmetric wave functions are associated with integer spin particles (photons, phonons, magnons, 4He atoms). These particles are called bosons, and obey the Bose—Einstein statistics. The antisymmetric wave functions are associated with half-integer spin particles (electrons, protons, atoms of 3He). These particles are called fermions, and obey the Fermi—Dirac statistics.KeywordsPartition FunctionQuantum StateClassical LimitDiatomic MoleculeOccupation NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.