Phase-equivalent energy-dependent potentials

Supersymmetric transformations, i.e., factorizations of the radial Schrodinger equation, are generalized to potentials with a linear dependence on energy. These transformations are equivalent to generalized Darboux transformations and do not affect the energy dependence of the potential. A pair of transformations allows the removal of a bound state without modification of the phase shift. The method is applied to the removal of the forbidden bound states of a deep energy-dependent alpha+O-16 potential generating a phase-equivalent shallow potential with an r(-2) repulsive core at the origin and the same energy dependence as the initial potential.