Kirkwood-Wigner Theorem

  • George D.J. Phillies
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


This Aside treats quantum corrections to the partition function of a nearly classical system. The argument given here follows very closely the derivation of Kirkwood [1], who showed that the procedure described below may be applied recursively to obtain corrections of arbitrarily high order in Planck’s constant h.From our point of view, the work has two major consequences for the constant C of the canonical-ensemble statistical weight, namely that:
  1. (1)

    the expectation of classical statistical mechanics agrees with the quantum expectation at low order in h; and

  2. (2)

    C is shown from quantum mechanics to contain an extra factor h 3N , 3N being the number of canonical coordinates (or canonically conjugate momenta) in the system.



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  1. [1]
    J. G. Kirkwood, Phys. Rev. 44, 31 (1933); 45, 116 (1934). Note also F. H. Stillinger’sIntroduction to John Gamble Kirkwood Collected Works, Volume 1. Quantum Statistics and Collective Phenomena, Gordon and Breach, New York (1965).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • George D.J. Phillies
    • 1
  1. 1.Department of Physics and Associated Biochemistry FacultyWorcester Polytechnic InstituteWorcesterUSA

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