The Analytical Solution of the Schr\"odinger Particle in Multiparameter Potential

TL;DR

This paper derives analytical solutions for the Schrödinger equation with a multiparameter potential using the asymptotic iteration method, providing numerical energy eigenvalues and eigenfunctions that align well with previous studies.

Contribution

It introduces an analytical approach to solve the Schrödinger equation with complex potentials using AIM and Pekeris approximation, extending previous work.

Findings

Numerical energy eigenvalues obtained for various quantum states.

Eigenfunctions corresponding to the multiparameter potential.

Results agree well with existing literature.

Abstract

In this study, we present analytical solutions of the Schr\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type approximation to the centrifugal potential. For any n and l (states) quantum numbers, we get the bound state energy eigenvalues numerically and the corresponding eigenfunctions.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.