Phase-equivalent potentials from supersymmetry: analytical results for a Natanzon-class potential

Abstract

Applying the techniques of supersymmetric quantum mechanics we determine closed algebraic expressions for potentials that are phase-equivalent with the generalized Ginocchio potential, which is a member of the rather general Natanzon-potential class. In particular, we discuss the elimination of bound states, the addition of one (or more) bound state at specific energies and also mention transformations that leave the spectrum unchanged. Our work represents the application of the abstract mathematical formalism developed recently for the modification of the spectrum of potentials without changing the S-matrix and the phase shifts. A new aspect of our work is that in addition to the new potential function, we give closed analytical expressions for the transformed Jost functions and bound-state wavefunctions. Furthermore, this work is the first example for generating phase-equivalent partners of a potential outside the relatively simple shape-invariant potential class.