New families of isospectral Hamiltonians

Abstract

A new procedure is developed for generating families of Hamiltonians which share exactly the same set of eigenvalues. The new method is related to the Marchenko equation in much the same manner as the method of Abraham and Moses [Phys. Rev. A 22, 1333 (1980)] is related to the Gel’fand-Levitan equation. The two procedures in general yield inequivalent new families of Hamiltonians when used to insert or delete states, but are equivalent (with a proper choice of parameters) when used to renormalize a state. The effect of the new procedure on reflection and transmission amplitudes and on the norming constants for bound states is compared with corresponding results using the Abraham-Moses and Darboux techniques.