PHASE-EQUIVALENT POTENTIALS FROM SUPERSYMMETRY - ANALYTICAL RESULTS FOR A NATANZON-CLASS POTENTIAL

Applying the techniques of supersymmetric quantum mechanics we determi ne closed algebraic expressions for potentials that are phase-equivale nt 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 stat e at specific energies and also mention transformations that leave the spectrum unchanged. Our work represents the application of the abstra ct mathematical formalism developed recently for the modification of t he 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 potent ial function, we give closed analytical expressions for the transforme d Jest functions and bound-state wavefunctions. Furthermore, this work is the first example for generating phase-equivalent partners of a po tential outside the relatively simple shape-invariant potential class.