![]() The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multisoliton solutions of the KdV equation are constructed. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. ![]() Familiar solvable potentials all have the property of shape invariance. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. ![]() In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems.
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