CYCLIC SHAPE INVARIANT POTENTIALS

Using supersymmetric quantum mechanics, we formulate the coupled non-l inear differential equations which give cyclic shape invariant potenti als, with eigenvalues consisting of p infinite sets of equally spaced energy levels, shifted with respect to each other. We study potentials in which the energy spacings are chosen using the logistic map and th e bifurcation route to chaos. (C) 1997 Elsevier Science B.V.