Analytical approximate bound state solution of Schr\"odinger equation in $D$-dimensions with a new mixed class of potential for arbitrary $\ell$-state via asymptotic iteration method

TL;DR

This paper derives approximate analytical solutions for the bound states of a D-dimensional Schrödinger equation with a new mixed potential using the asymptotic iteration method, providing energy spectra and eigenfunctions for arbitrary angular momentum states.

Contribution

It introduces a novel mixed potential and applies the asymptotic iteration method to obtain approximate solutions for arbitrary angular momentum states in D-dimensions.

Findings

Derived energy spectra and eigenfunctions for the potential.

Showed the potential's capability to reproduce known potentials.

Solutions are in excellent agreement with existing literature.

Abstract

The bound state solutions of the $D$-dimensional Schr\"{o}dinger equation for new mixed class of potential, $V(r)=\frac{V_1}{r^2}+\frac{V_2e^{-\alpha r}}{r}+V_3coth\alpha r+V_4\,,$ are studied within the framework of the Pekeris approximation for any arbitrary $\ell$-state. Asymptotic iteration method (AIM) is used for the work. The energy spectrum are obtained as well as their corresponding normalized eigenfunctions are derived in terms of generalized hypergeometric functions $\,_{2}F_{1}(a,b,c;z)$. It is shown that using the Pekeris approximation, present potential model is very much capable of deriving other well known potentials quite easily and corresponding solutions are in excellent agreement with the previous work carried out in literature.