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

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Arda A., Sever R.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.50, no.4, pp.971-980, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1007/s10910-011-9944-y
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.971-980
  • Keywords: Exact solution, Bound states, Laplace transform, Pseudoharmonic potential, Mie-type potential, Schrodinger equation, HARMONIC-OSCILLATOR, SPECTROSCOPY, QUANTIZATION
  • Middle East Technical University Affiliated: Yes


Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrodinger 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 wave-functions 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.