Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary $l$ state

TL;DR

This paper derives analytical solutions for the radial Schrödinger equation with the Woods-Saxon potential for any angular momentum state using the Nikiforov-Uvarov method and Pekeris approximation.

Contribution

It provides a general analytical approach to solve the Schrödinger equation with the Woods-Saxon potential for arbitrary $l$ states, including energy eigenvalues and eigenfunctions.

Findings

Explicit energy eigenvalues for various quantum numbers

Analytical eigenfunctions derived for arbitrary $l$

Method applicable to nuclear physics problems

Abstract

In this work, the analytical solution of the radial Schr\"{o}dinger equation for the Woods-Saxon potential is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary $l$ states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of $n$ and $l$ quantum numbers.