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Exact solutions of the Schrödinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials

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Abstract

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrödinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wavefunctions of the above potentials. It is also given numerical results for the bound states of two diatomic molecular potentials, and compared the results with the ones obtained in literature.

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Authors and Affiliations

  1. Department of Physics Education, Hacettepe University, 06800, Ankara, Turkey

    Altuğ Arda

  2. Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

    Ramazan Sever

Authors
  1. Altuğ Arda
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  2. Ramazan Sever
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Correspondence to Altuğ Arda.

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Arda, A., Sever, R. Exact solutions of the Schrödinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials. J Math Chem 50, 971–980 (2012). https://doi.org/10.1007/s10910-011-9944-y

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  • DOI: https://doi.org/10.1007/s10910-011-9944-y

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