On- and off-shell Jost functions and their integral representations

摘要

By judicious exploitation of the transpose operator relation in conjunction with thedifferential equations of special functions of mathematical physics, integral representations of the on- and off-shell Jost functions are derived from the particular integrals of the inhomogeneous Schr??dinger equation. Using the particular integral of the inhomogeneous Schr??dinger equation, exact analytical expressions for the Coulomb and Coulomb plus Yamaguchi off-shell Jost solutions are constructed in the maximal reduced form. As a case study, the limiting behaviours and the on-shell discontinuities of the Coulomb plus Yamaguchi Jost solutions are verified numerically.