Solutions of the D-dimensional Schrodinger equation with the hyperbolic Poschl Teller potential plus modified ring shaped term

TL;DR

This paper analytically solves the D-dimensional Schrödinger equation with a hyperbolic Pöschl-Teller and ring-shaped potential using the Nikiforov-Uvarov method, deriving explicit energy levels and wave functions.

Contribution

It introduces an exact solution approach for the D-dimensional Schrödinger equation with combined hyperbolic Pöschl-Teller and ring-shaped potentials using the NU method.

Findings

Explicit energy eigenvalues derived

Wave functions expressed in closed form

Solutions applicable to higher-dimensional quantum systems

Abstract

In this paper, we solve the D-dimensional Schr\"odinger equation with hyperbolic Poschl-Teller potential plus a generalized ring-shaped potential. After the separation of variable in the hyperspherical coordinate. We used Nikiforov-Uvarov (NU) method to solve the resulting radial equation and obtain explicitly the energy level and the corresponding wave function in closed form. The solutions to the angular part are solved using the NU approach as well.