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Integrals of the motion and exact solutions of the problem of two dispersing delta-wells

  • Atoms, Spectra, Radiation
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Abstract

An exact solution is analyzed for the analogs of bound and scattering states in a nonstationary quantum mechanical system whose potential has the form of two dispersing delta-wells. For the delta-potentials explicit (in the form of operator kernels) expressions are found for the integrals of the motion that depend on time and transform to the known integrals of the motion for a free quantum particle as the interaction force with the potential approaches zero.

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References

  1. K. Husimi, Prog. Theor. Phys. 9, 381 (1953).

    MATH  MathSciNet  Google Scholar 

  2. J. Schwinger, Phys. Rev. 91, 728 (1953).

    ADS  MathSciNet  Google Scholar 

  3. R. Feynman, Phys. Rev. 84, 108 (1951).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. V. P. Ermakov, Univ. Izv. (Univ. Sv. Vladimira, Kiev) XX(9), 1 (1880).

    Google Scholar 

  5. H. R. Lewis, Phys. Rev. Lett. 18, 510 (1966).

    ADS  Google Scholar 

  6. H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969).

    MathSciNet  Google Scholar 

  7. I. A. Malkin, V. I. Man’ko, and D. A. Trifonov, Phys. Rev. D 2, 1371 (1970).

    Article  ADS  Google Scholar 

  8. I. A. Malkin and V. I. Man’ko, Phys. Lett. 32, 243 (1970).

    Google Scholar 

  9. I. A. Malkin, V. I. Man’ko, and D. A. Trifonov, J. Math. Phys. 14, 576 (1973).

    Article  Google Scholar 

  10. I. A. Malkin and V. I. Man’ko, Zh. Éksp. Teor. Fiz. 58, 721 (1970) [Sov. Phys. JETP 31, 386 (1970)].

    Google Scholar 

  11. C. Groshe, Phys. Lett. A 182, 28 (1993); Ann. Phys. (N.Y.) 2, 557 (1993).

    ADS  MathSciNet  Google Scholar 

  12. M. Moshinsky, Am. J. Phys. 44, 1037 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  13. W. Damert, Am. J. Phys. 43, 531 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  14. V. V. Dodonov, V. I. Man’ko, and D. E. Nikonov, Phys. Lett. A 162, 359 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  15. S. K. Zhdanov and A. S. Chikhachev, Dokl. Akad. Nauk SSSR 218, 1323 (1974).

    Google Scholar 

  16. A. S. Chikhachev, Zh. Éksp. Teor. Fiz. 107, 1153 (1995) [JETP 80, 641 (1995)].

    Google Scholar 

  17. N. M. Nussenzweig, in Symmetries in Physics (Proc. of the I International Symposium Held in Honor of Prof. M. Moshinsky, 1991, A. Frank and K. B. Wolf (eds.), Springer-Verlag, Berlin, Heidelberg (1992).

    Google Scholar 

  18. I. A. Malkin and V. I. Man’ko, Dynamic Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  19. W. Dappen, J. Phys. B 10, 2399 (1977).

    ADS  Google Scholar 

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Authors and Affiliations

  1. P. N. Lebedev Physics Institute, Russian Academy of Sciences, 117924, Moscow, Russia

    V. I. Man’ko

  2. Salyut Design Bureau, M. V. Khrunichev State Space Scientific-Production Center, 101000, Moscow, Russia

    A. S. Chikhachev

Authors
  1. V. I. Man’ko
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  2. A. S. Chikhachev
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Additional information

Zh. Éksp. Teor. Fiz. 113, 606–614 (February 1998)

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Man’ko, V.I., Chikhachev, A.S. Integrals of the motion and exact solutions of the problem of two dispersing delta-wells. J. Exp. Theor. Phys. 86, 335–339 (1998). https://doi.org/10.1134/1.558462

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  • DOI: https://doi.org/10.1134/1.558462

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