Solutions to the modified Poschl-Teller Potential in D-dimensions

TL;DR

This paper presents an approximate analytical solution to the D-dimensional Schrödinger equation with the modified Pöschl-Teller potential, including normalization and expectation value calculations, using the Nikiforov-Uvarov method.

Contribution

It introduces an approximate solution method for the D-dimensional Schrödinger equation with the modified Pöschl-Teller potential employing the Nikiforov-Uvarov technique.

Findings

Derived explicit wavefunctions and energy eigenvalues.

Computed normalization constants for the potential.

Calculated expectation values using Feynman-Hellmann theorem.

Abstract

An approximate solution of the $D$-dimensional Schr$\ddot{o}$dinger equation with the modified P$\ddot{o}$schl-Teller potential is obtained with an approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given using the conventional Nikiforov-Uvarov method. The normalization constants for the P$\ddot{o}$schl-Teller potential are also computed. The expectation values $<r^{-2}>$,$<V(r)>$, are also obtained using the Feynman-Hellmann theorem.