Journal of Statistical Physics

, Volume 40, Issue 1–2, pp 329–360 | Cite as

Limit theorem for the distribution of eigenvalues of the operator of energy

  • M. S. Goldstein
Articles

Abstract

We prove the central limit theorem for the distribution of eigenvalues of the energy operator of a continuous quantum mechanical system. We consider one-dimensional and multidimensional systems.

Key words

Limit theorem eigenvalues 

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References

  1. 1.
    J. Ginibre,J. Math. Phys. 6:238–251 (1965).Google Scholar
  2. 2.
    J. Ginibre,J. Math. Phys. 6:252–262 (1965).Google Scholar
  3. 3.
    J. Ginibre,J. Math. Phys. 9:1432–1446 (1965).Google Scholar
  4. 4.
    Yu. M. Suchov,Mat. Sb. (1970).Google Scholar
  5. 5.
    Yu. M. Suchov,Tr. Mosk. Mat. Ova. 26:151–179 (1972).Google Scholar
  6. 6.
    Yu. M. Suchov,C. R. Acad. Sci. Paris Ser. A. 279:433–434, 475–477 (1974).Google Scholar
  7. 7.
    A. M. Khaifina,Mat. Sb. 80:3–51 (1969).Google Scholar
  8. 8.
    Yu. Damyan,Teor. Mat. Fiz. 34:341–352 (1978).Google Scholar
  9. 9.
    A. Khaitov,Dokl. Akad. Nauk. Uzb. SSR, No. 1, 12–15 (1980).Google Scholar
  10. 10.
    D. Ruel,Statistical Mechanics (1969).Google Scholar
  11. 11.
    R. H. Cameron,J. Math. Phys. XXXIX(1), 126–140 (1960).Google Scholar
  12. 12.
    R. H. Cameron,J. Anal. Math. X:287–361 (1962).Google Scholar
  13. 13.
    V. S. Vladimirov,Equations of Mathematical Physics (in Russian), Moscow (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • M. S. Goldstein
    • 1
  1. 1.Tashkent State UniversityTashkentUSSR

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