Analytic transition matrix for the Manning-Rosen potential in all partial waves

Abstract

The off-shell Jost and physical solutions of the Manning-Rosen potential are derived by adapting two different approaches to the problem. In contrast to the semi-classical approaches to the problem we construct exact analytical expression of the off-shell transition matrix for the Manning-Rosen potential in all partial waves by adapting pure quantum mechanical method. Our constructed expressions are in their maximal reduced form and consistent with respect to their limiting behaviors. The off-shell transition matrix satisfies the unitarity relation for positive energy. To authors’ knowledge, these results for the off-shell quantities have not yet been discussed in the literature.