Generalized potentials: Free particle, harmonic, and morse partner potentials

In this work, we propose a very simple procedure to find the partner to spe cific potentials. According to our method, partner potentials are those obt ained in the generalization of standard potentials, for which they are gene ralized potentials whose Hamiltonian match the so-called isospectral Hamilt onian. The proposed approach is straightforward and basically takes into co nsideration the use of three well-established relationships: The first one is used to identify the particular potential; the second, to find the adjoi nt or modified potential; and the third, to obtain the corresponding genera lized or partner potential. As a useful application of the proposed procedu re, we give explicitly the generalized and modified free-particle, harmonic oscillator, and Morse one-dimensional potentials. As expected, it is shown that the adjoint and partner potentials are isospectral with respect to th e particular or former potential. This procedure can be easily applied to t he generalization of any other known potential, as well as to obtain new po tentials that can be advantageously used for modeling important quantum int eractions. (C) 1999 John Wiley & Sons, Inc.