Theoretical and Mathematical Physics

, Volume 98, Issue 1, pp 34–38 | Cite as

The semiclassical approximation in quantum mechanics. A new approach

  • V. G. Bagrov
  • V. V. Belov
  • M. F. Kondrat'eva
Article
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Abstract

It is shown that the semiclassical approximation in quantum mechanics is equivalent to replacement of the Schrödinger equation by a finite closed system of first-order ordinary differential equations with initial conditions that satisfy special restrictions.

Keywords

Differential Equation Quantum Mechanic Ordinary Differential Equation Closed System Special Restriction 
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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References

  1. 1.
    H. Green,Matrix Mechanics, Groningen (1965).Google Scholar
  2. 2.
    V. P. Maslov,Theorie des Perturbations et Methodes Asymptotics, Ounod, Paris (1972).Google Scholar
  3. 3.
    V. P. Maslov and M. V. Fedoriuk,Semiclassical Approximation in Quantum Mechanics, Reidel, Dordrecht (1981).Google Scholar
  4. 4.
    V. P. Maslov,Asymptotic Methods and Perturbation Theory [in Russian], Nauka, Moscow (1988).Google Scholar
  5. 5.
    V. S. Buslaev,Funktsional. Analiz i Ego Prilozhen.,3, 17 (1969).Google Scholar
  6. 6.
    V. V. Kucherenko,Izv. Akad. Nauk SSSR, Ser. Mat.,38, 625 (1974).Google Scholar
  7. 7.
    J. Leray,Lagrangian Analysis and Quantum Mechanics, Cambridge, Mass. (1981).Google Scholar
  8. 8.
    S. Yu. Dobrokhotov and V. P. Maslov, in:Modern Problems of Mathematics, Vol. 17 [in Russian], VINITI (1980), p. 3.Google Scholar
  9. 9.
    V. G. Danilov and V. P. Maslov, in:Modern Problems of Mathematics, Vol. 6 [in Russian], VINITI (1975), p. 5.Google Scholar
  10. 10.
    A. S. Mishchenko, B. Yu. Sternin, and V. E. Shatalov,Lagrangian Manifolds and the Canonical Operator Method [in Russian], Nauka, Moscow (1978).Google Scholar
  11. 11.
    V. V. Belov and S. Yu. Dobrokhotov,Dokl. Akad. Nauk SSSR,298, 1037 (1988).Google Scholar
  12. 12.
    V. V. Belov and S. Yu. Dobrokhotov, “Semiclassical Maslov asymptotics in spectral quantum problems corresponding to partly integrable Hamiltonian systems,” Preprint [in Russian], V. A. Steklov Mathematics Institute, USSR Academy of Sciences, Moscow (1988).Google Scholar
  13. 13.
    M. V. Karasev and V. P. Maslov,Izv. Akad. Nauk SSSR, Ser. Mat.,47, 999 (1983).Google Scholar
  14. 14.
    V. V. Dodonov and V. P. Man'ko,Tr. FIAN,183, 5.Google Scholar
  15. 15.
    V. G. Bagrov, V. V. Belov, and I. M. Ternov,Teor. Mat. Fiz.,50, 390 (1982).Google Scholar
  16. 16.
    V. G. Bagrov, V. V. Belov, and I. M. Ternov,J. Math. Phys.,24, 2855 (1983).Google Scholar
  17. 17.
    A. M. Rogova, Paper No. 129-V9 [in Russian], deposited at VINITI, Moscow (1992).Google Scholar
  18. 18.
    V. V. Belov and V. P. Maslov,Dokl. Akad. Nauk SSSR,311, 849 (1990).Google Scholar
  19. 19.
    V. V. Belov and M. F. Kondrat'eva,Teor. Mat. Fiz.,92, 41 (1992).Google Scholar
  20. 20.
    S. K. Wong,Nuovo Cimento A,65, 689 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. G. Bagrov
  • V. V. Belov
  • M. F. Kondrat'eva

There are no affiliations available

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