Journal of Molecular Modeling

, Volume 19, Issue 5, pp 2007–2014 | Cite as

Three–dimensional effective mass Schrödinger equation: harmonic and Morse-type potential solutions

  • G. OvandoEmail author
  • J. Morales
  • J. L. López-Bonilla
Original Paper


In this work, a scheme to generate exact wave functions and eigenvalues for the spherically symmetric three-dimensional position-dependent effective mass Schrödinger equation is presented. The methodology is implemented by means of separation of variables and point canonical transformations that allow to recognize a radial dependent equation with important differences as compared with the one-dimensional position dependent mass problem, which has been widely studied. This situation deserves to consider the boundary conditions of the emergent problem. To obtain specific exact solutions, the methodology requires known solutions of ordinary one-dimensional Schrödinger equations. We have preferred those applications that use the harmonic oscillator and the Morse oscillator solutions.


Harmonic potential Morse potential Position-dependent effective mass Three dimensional Schrödinger equation 



G. O. and J. M. are thankful for the support received from CONACYT-MEXICO through the SNI program.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.CBI—Area de Física Atómica Molecular AplicadaUniversidad Autónoma Metropolitana—AzcapotzalcoMexico CityMexico
  2. 2.Instituto Politécnico Nacional, ESIME-ZacatencoMexico CityMexico

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