Non-Central Potentials, Exact Solutions and Laplace Transform Approach

TL;DR

This paper derives exact bound state solutions and wave functions for various non-central potentials in the Schrödinger equation using the Laplace transform approach, confirming consistency with existing results and providing new numerical insights.

Contribution

It introduces a Laplace transform method to solve the Schrödinger equation for multiple non-central potentials, offering exact solutions and numerical results.

Findings

Analytical solutions for several non-central potentials.

Energy spectra for Hartmann, Kratzer, and ring-shaped oscillators.

Numerical results for modified non-central potential.

Abstract

Exact bound state solutions and the corresponding wave functions of the Schr\"odinger equation for some non-central potentials including Makarov potential, modified-Kratzer plus a ring-shaped potential, double ring-shaped Kratzer potential, modified non-central potential and ring-shaped non-spherical oscillator potential are obtained by using the Laplace transform approach. The energy spectrums of the Hartmann potential, modified-Kratzer potential and ring-shaped oscillator potential are also briefly studied as special cases. It is seen that our analytical results for all these potentials are consistent with those obtained by other works. We also give some numerical results obtained for the modified non-central potential for different values of the related quantum numbers.