Russian Physics Journal

, Volume 52, Issue 12, pp 1339–1351 | Cite as

Method of comparison equations and generalized Ermakov’s equation

  • A. KamenshchikEmail author
  • M. Luzzi
  • G. Venturi


Ermakov’s equation semiclassical approach comparison functions 


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  1. 1.
    L. I. Schiff, Quantum mechanics, McGraw Hill, New York (1968).Google Scholar
  2. 2.
    M. V. Berry and K. E. Mount, Rept. Prog. Phys., 35, 315 (1972).CrossRefADSGoogle Scholar
  3. 3.
    B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York (1965).zbMATHGoogle Scholar
  4. 4.
    F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York (1974).Google Scholar
  5. 5.
    R. B. Dingle, Asymptotic Expansions: Their Derivation and Interpretation, Academic Press, London (1973).zbMATHGoogle Scholar
  6. 6.
    S. C. Miller, Jr. and R. H. Good Jr., Phys. Rev., 91, 174 (1953).zbMATHCrossRefMathSciNetADSGoogle Scholar
  7. 7.
    R. B. Dingle, Appl. Sci. Res., B5, 345 (1956).MathSciNetGoogle Scholar
  8. 8.
    V. P. Ermakov, Univ. Izv. Kiev, Series III, 9, 1 (1880).Google Scholar
  9. 9.
    E. Pinney, Proc. Amer. Math. Soc., 1, 681 (1950).CrossRefMathSciNetGoogle Scholar
  10. 10.
    R. E. Langer, Phys. Rev., 51, 669 (1937).zbMATHCrossRefADSGoogle Scholar
  11. 11.
    J. Martin and D. J. Schwarz, Phys. Rev., D67, 083512 (2003); S. Habib, A. Heinen, K. Heitmann, G. Jungman, and C. Molina-Paris, Phys. Rev., D70, 083507 (2004); R. Casadio, F. Finelli, M. Luzzi, and G. Venturi, Phys. Rev., D71, 043517 (2005).MathSciNetADSGoogle Scholar
  12. 12.
    R. Casadio, F. Finelli, A. Kamenshchik, M. Luzzi, and G. Venturi, J. Cosm. Astropart. Phys., 04, 011 (2006); R. Casadio, F. Finelli, M. Luzzi, and G. Venturi, Phys. Rev., D72, 103516 (2005); R. Casadio, F. Finelli, M. Luzzi, and G. Venturi, Phys. Lett., B625, 1 (2005).CrossRefADSGoogle Scholar
  13. 13.
    I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York (1980).Google Scholar
  14. 14.
    H. R. Lewis, J. Math. Phys., 9, 1976 (1968).zbMATHCrossRefADSGoogle Scholar
  15. 15.
    W. E. Milne, Phys. Rev., 35, 863 (1930).CrossRefADSGoogle Scholar
  16. 16.
    P. Espinosa, Ermakov–Lewis dynamic invariants with some applications, MS Thesis, Instituto de Física – Universidad de Guanajuato, Leòn (2000).Google Scholar
  17. 17.
    U. Fano and A. R. P. Rau, Atomic Collisions and Spectra, Academic Press, Orlando (1986).Google Scholar
  18. 18.
    F. Finelli, G. P. Vacca, and G. Venturi, Phys. Rev., D58, 103514 (1998); C. Bertoni, F. Finelli, and G. Venturi, Phys. Lett., A237, 331 (1998); F. Finelli, A. Gruppuso, and G. Venturi, Class. Quantum Grav., 16, 3923 (1999); H. Rosu, P. Espinosa, and M. Reyes, Nuovo Cimento, B114, 1435 (1999); R. M. Hawkins and J. E. Lidsey, Phys. Rev., D66, 023523 (2002).ADSGoogle Scholar
  19. 19.
    C. J. Eliezer and A. Gray, SIAM J. Appl. Math., 30, 46 (1976).CrossRefMathSciNetGoogle Scholar
  20. 20.
    M. V. Ioffe and H. J. Korsch, Phys. Lett., A311, 200 (2003).MathSciNetADSGoogle Scholar
  21. 21.
    J. R. Ray and J. L. Reid, Phys. Lett., A71, 317 (1979).MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.L. D. Landau Institute for Theoretical Physics of the Russian Academy of SciencesMoscowRussia
  2. 2.Dipartimento di FisicaUniversità di Bologna and I.N.F.N., Sezione di BolognaBolognaItaly

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