Exact Solutions of the Schrödinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials

Details Exact Solutions of the Schrödinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials Exact Solutions of the Schrödinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials

2012-02-20

arxiv.org/abs/1202.4268v1

J. Math. Chem. 50, 971 (2012)

Physics

Mathematical Physics

15 pages, 2 figures

Scientific paper

10.1007/s10910-011-9944-y

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger 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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