Bound State Solutions of Schr\"odinger Equation for a more general Woods-Saxon Potential with Arbitrary l - state

TL;DR

This paper derives bound state solutions for the Schrödinger equation with a generalized Woods-Saxon potential, expressing wave functions via Jacobi polynomials and exploring special cases like Hulthen and standard Woods-Saxon potentials.

Contribution

It introduces a more general form of the Woods-Saxon potential and provides analytical solutions for arbitrary angular momentum states, including special cases.

Findings

Wave functions expressed in Jacobi polynomials

Energy spectra derived for special potential cases

Unified approach for different potential forms

Abstract

The energy spectra and the wave function depending on the c-factor are investigated for a more general Woods-Saxon potential (MGWSP) with an arbitrary l - state. The wave functions are expressed in terms of the Jacobi polynomials. Two potentials are obtained from this MGWSP as special cases. These special potentials are Hulthen and the standard Woods-Saxon potentials. We also discuss the energy spectrum and wave function for the special cases.