The Ideal Fermi Gas

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


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


Fermi Energy Landau Level Free Fermion Zero Field Free Boson 
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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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