Scattering, bound and quasi-bound states of the generalized symmetric Woods-Saxon potential

TL;DR

This paper provides exact analytical solutions for the Schrödinger equation with a generalized symmetric Woods-Saxon potential, exploring scattering, bound, and quasi-bound states, and deriving conditions for transmission resonance.

Contribution

It introduces new analytical solutions and resonance conditions for the generalized symmetric Woods-Saxon potential in quantum mechanics.

Findings

Analytical expressions for reflection and transmission coefficients.

Identification of resonance conditions at quasi-bound state energies.

Correlation between potential parameters and scattering properties.

Abstract

The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients are analytically obtained. Then, the correlations between the potential parameters and the reflection-transmission coefficients are investigated, and a transmission resonance condition is derived. Occurrence of the transmission resonance has been shown when incident energy of the particle is equal to one of the resonance energies of the quasi-bound states.