Isospectral potentials from modified factorization

Abstract

Factorization of quantum-mechanical potentials has a long history extending back to the earliest days of the subject. In the present article, the nonuniqueness of the factorization is exploited to derive new isospectral nonsingular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.