The Ideal Fermi Gas

  • Silvio R. A. Salinas
Part of the Graduate Texts in Contemporary Physics book series (GTCP)

Abstract

Given the volume, the temperature, and the chemical potential, the grand partition function for free fermions may be written in the form
$$In \equiv \left( {T,V,\mu } \right) = \sum\limits_j {In} \left\{ {1 = \exp [ - \beta \left( {{\varepsilon _j} - \mu } \right)]} \right\},$$
(9.1)
where the sum is over all single-particle quantum states. The expected value of the occupation number of an orbital is given by
$$\left\langle {{n_j}} \right\rangle = \frac{1}{{\exp [\beta \left( {{\varepsilon _j} - \mu } \right)] + 1}},$$
(9.2)
which is very often called the Fermi—Dirac distribution. The connection with thermodynamics, in the limit V → ∞, is provided by the grand thermodynamic potential,
$$\Phi \left( {T,V,\mu } \right) = - \frac{1}{\beta }In \equiv \left( {T,V,\mu } \right).$$
(9.3)

Keywords

Fermi Energy Landau Level Free Fermion Zero Field Free Boson 
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

Authors and Affiliations

  • Silvio R. A. Salinas
    • 1
  1. 1.Instituto de FisicaUniversidade de São PaoloSão PaoloBrazil

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