Theoretical and Mathematical Physics

, Volume 88, Issue 1, pp 699–706 | Cite as

Oscillator with centrifugal barrier. Inverse problem

  • V. B. Gostev
  • A. R. Frenkin


Thus, contrary to an assertion made in the literature ([16], p. 113), we have succeeded in finding a physically acceptable way of continuing a solution of the Schrödinger equation through the potential singularity λx−2, and by means of this continuation we have augmented the classical theory of inverse problems of quantum mechanics [16] with a new solution, finding moreover a nontrivial behavior of the correction to the potential.


Quantum Mechanic Inverse Problem Classical Theory Potential Singularity Centrifugal Barrier 
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Literature Cited

  1. 1.
    M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, New York (1978), Chap. 12.Google Scholar
  2. 2.
    E. Harrel, Ann. Phys. (N.Y.),105, 379 (1977).Google Scholar
  3. 3.
    R. E. Moss, Am. J. Phys.,55, 397 (1987).Google Scholar
  4. 4.
    I. Dittrich and P. Exner, J. Math. Phys.,26, 2000 (1985).Google Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Nonrelativistic Theory, 3rd ed., Pergamon Press, Oxford (1977). (The pagination in the text corresponds to the Russian edition published by Nauka, Moscow in 1989.)Google Scholar
  6. 6.
    A. M. Perelomov, Generalized Coherent States and Applications [in Russian], Nauka, Moscow (1987), pp. 164–175.Google Scholar
  7. 7.
    V. B. Gostev, V. S. Mineev, and A. R. Frenkin, Teor. Mat. Fiz.,68, 45 (1986).Google Scholar
  8. 8.
    V. B. Gostev and A. R. Frenkin, Vestn. Mosk. Univ. Fiz. Astron., Ser. 3,28, 85 (1987).Google Scholar
  9. 9.
    V. B. Gostev and A. R. Frenkin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 10, 85 (1989).Google Scholar
  10. 10.
    F. Calogero, J. Math. Phys.,10, 2191 (1969).Google Scholar
  11. 11.
    J. Klauder, Acta Phys. Austriaca Suppl.,11 341, (1973).Google Scholar
  12. 12.
    I. A. Malkin and V. I. Man'ko, Dynamical Symmetry and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979), p. 109.Google Scholar
  13. 13.
    V. B. Gostev, V. K. Peres-Fernandes, A. R. Frenkin, and G. A. Chizhov, Vestn. Mosk. Univ., Fiz. Astron., Ser. 3,30, 22 (1989).Google Scholar
  14. 14.
    F. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 2, McGraw Hill, New York (1953).Google Scholar
  15. 15.
    V. V. Dodonov and V. I. Man'ko, Tr. Fiz. Inst. Akad. Nauk,183, 3 (1987).Google Scholar
  16. 16.
    K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer, Berlin (1977).Google Scholar
  17. 17.
    V. B. Gostev and A. R. Frenkin, Teor. Mat. Fiz.,62, 472 (1985).Google Scholar
  18. 18.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover (1964).Google Scholar
  19. 19.
    J. Von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton (1955).Google Scholar
  20. 20.
    P. B. Abraham and H. E. Moses, Phys. Rev. A,22, 1333 (1980).Google Scholar
  21. 21.
    V. B. Gostev, V. S. Mineev, and A. R. Frenkin, Teor. Mat. Fiz.,56, 74 (1983).Google Scholar
  22. 22.
    V. B. Gostev and A. R. Frenkin, Teor. Mat. Fiz.,74, 247 (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • V. B. Gostev
  • A. R. Frenkin

There are no affiliations available

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