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Introduction to Quantum Statistics of Degenerate Bose Systems

  • Franz Mohling

Abstract

Historically, the first-known example of a Bose system was the photon gas. In 1924, S.N. Bose1 first showed that one could understand Planck’s equation for the energy-density of black-body radiation from a “quantum-statistical” point of view. His basic assumptions were that many light quanta could occupy the same quantum-mechanical element h3 of phase space and that the light quanta are indistinguishable. This led him, with the aid of a simple statistical mechanical argument, to the important result for the average number of quanta in a single state:
$$\left \langle N_i \right \rangle\ =\frac{\textup{exp}(-\beta\omega_i)}{1\ -\ \textup{exp}(-\beta\omega_i)}$$
(1)
where \(\left\langle {{N_i}} \right\rangle \; = \frac{{exp( - \beta {\omega _i})}}{{1\; - \;exp( - \beta {\omega _i})}}\). By a “simple state” was meant an element of phase space Ωσ3P i which equals h3 (Ω= volume of system). This simple formula could then be used to derive the thermodynamic properties of blackbody radiation by elementary means.

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Copyright information

© Plenum Press 1966

Authors and Affiliations

  • Franz Mohling
    • 1
  1. 1.University of ColoradoBoulderUSA

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