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

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.

15 pages, 2 figures

References in corpus (3)

• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass
• Alternative Solution of the Path Integral for the Radial Coulomb Problem

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