International Journal of Theoretical Physics

, Volume 52, Issue 1, pp 88–95 | Cite as

Time-Dependent Gaussian Solution for the Kostin Equation Around Classical Trajectories

  • F. Haas
  • J. M. F. Bassalo
  • D. G. da Silva
  • A. B. Nassar
  • M. Cattani
Article

Abstract

The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of mass follows the dynamics of a classical particle under the external potential and a damping proportional to the velocity; the width of the wave packet satisfy a non-conservative Pinney equation. An appropriate perturbation theory is developed for the free particle case, solving the long standing problem of finding analytic expressions for square integrable solutions of the free Kostin equation. The associated Wigner function is also studied.

Keywords

Kostin equation Dissipative quantum mechanics Damped Pinney equation 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • F. Haas
    • 1
  • J. M. F. Bassalo
    • 2
  • D. G. da Silva
    • 3
  • A. B. Nassar
    • 4
  • M. Cattani
    • 5
  1. 1.Departamento de FísicaUniversidade Federal do ParanáCuritibaBrazil
  2. 2.Fundação MinervaBelémBrazil
  3. 3.Escola Munguba do JariAmapáBrazil
  4. 4.Extension Program—Department of SciencesUniversity of CaliforniaLos AngelesUSA
  5. 5.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

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