Alternative analysis to perturbation theory in quantum mechanics

Dyson series in matrix form
  • J. Martínez-Carranza
  • F. Soto-Eguibar
  • H. Moya-Cessa
Regular Article

Abstract

We develop an alternative approach to the time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function; additionally we can analyze the time evolution of the system for any initial condition, which may be bothersome in the standard method. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.

Keywords

Quantum Optics 

References

  1. 1.
    E. Schrödinger, Phys. Rev. 28, 1049 (1926) ADSCrossRefGoogle Scholar
  2. 2.
    E. Schrödinger, Ann. Phys. 80, 361 (1926)CrossRefGoogle Scholar
  3. 3.
    J.L. Powell, Quantum Mechanics (Addison-Wesley, Reading, 1961)Google Scholar
  4. 4.
    P.M. Morse, Phys. Rev. 34, 57 (1929)ADSCrossRefGoogle Scholar
  5. 5.
    A. Moliton, Solid-State Physics for Electronics (Wiley, 2009)Google Scholar
  6. 6.
    J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994)Google Scholar
  7. 7.
    B. Simon, Bull. Amer. Math. Soc. 24, 303 (1991)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    M. Znojil, J. Phys. A 30, 8771 (1997) MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    W. Hai et al., Phys. Rev. A 61, L79 (2000)CrossRefGoogle Scholar
  10. 10.
    Z. Yun-Hui et al., Chin. Phys. B 17, 1720 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    H. Moya-Cessa, M. Fernández-Guasti, Phys. Lett. A 311, 1 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    S.M. Dutra, Cavity quantum electrodynamics (Wiley, 2005)Google Scholar
  13. 13.
    F.J. Dyson, Phys. Rev. 75, 486 (1949)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    W. Greiner, J. Reinhardt, Field Quantization (Springer, 1996)Google Scholar
  15. 15.
    P. Roman, Advanced Quantum Theory (Addison-Wesley, Reading, 1965)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • J. Martínez-Carranza
    • 1
  • F. Soto-Eguibar
    • 1
  • H. Moya-Cessa
    • 1
  1. 1.Instituto Nacional de AstrofisicaOptica y ElectronicaPuebla, Pue.Mexico

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