The Hulthen Potential in D-dimensions

TL;DR

This paper derives approximate solutions to the Schrödinger equation with the Hulthén potential in D-dimensions, employing the Nikiforov-Uvarov method and calculating normalization and expectation values.

Contribution

It introduces an exponential approximation for the centrifugal term and applies the Nikiforov-Uvarov method to solve the hyper-radial equation in D-dimensions.

Findings

Derived approximate energy eigenvalues and wavefunctions.

Computed normalization constants for the Hulthén potential.

Calculated expectation values using the Feynman-Hellmann theorem.

Abstract

An approximate solution of the Schrodinger equation with the Hulth$\acute{e}$n potential is obtained in D-dimensions with an exponential 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 Hulth$\acute{e}$n potential are also computed. The expectation values $<r^{-2}>$,$<V(r)>$, are also obtained using the Feynman-Hellmann theorem.