Introduction to Statistical Physics pp 141-159 | Cite as

# The Ideal Quantum Gas

Chapter

## Abstract

A quantum system of
where
which indicates that the quantum state of the system does not alter if we change the coordinates of two particles. The

*N*identical particles is described by the wave function$$\Psi = \Psi ({q_1}, \ldots {q_N}),$$

(8.1)

*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)

**symmetric**wave functions are associated with**integer spin**particles (photons, phonons, magnons,^{4}He 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^{3}He). These particles are called**fermions**, and obey the**Fermi—Dirac statistics**.## Keywords

Partition Function Quantum State Classical Limit Diatomic Molecule Occupation Number
These 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.

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## Copyright information

© Springer Science+Business Media New York 2001