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Noninteracting Particles

  • Walter T. GrandyJr.
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 19)

Abstract

When we set  = exp(−βĤ N ) in Eq. (4-105) we obtain a completely general expression for the canonical partition function describing an N-particle system in thermal equilibrium:
$${\text{Tr}}{{e}^{ - }}^{{\beta {{{\widehat{{\text{H}}}}}_{N}}}} = \frac{1}{{N!}}{{\sum\limits_{{{{\lambda }_{1}} \cdots {{\lambda }_{N}}}} {\left[ {\sum\limits_{{P'}} {{{\varepsilon }^{{P'}}}\hat{P}'} \left\langle {{{\lambda }_{1}} \cdots {{\lambda }_{N}}\left| {{{e}^{ - }}^{{\beta {{{\widehat{{\text{H}}}}}_{N}}}}} \right|{{{\lambda '}}_{1}} \cdots {{{\lambda '}}_{N}}} \right\rangle } \right]} }_{{{{{\lambda '}}_{i}} = {{{\lambda '}}_{1}}_{i}}}}, $$
where Ĥ N is the N-particle Hamiltonian, including interactions.

Keywords

Partition Function Pauli Principle Canonical Partition Function Boltzmann Statistic Noninteracting Particle 
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

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Walter T. GrandyJr.
    • 1
  1. 1.Department of Physics and AstronomyUniversity of WyomingUSA

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