A NEW SUPERSYMMETRIC VERSION OF THE ABRAHAM-MOSES METHOD FOR SYMMETRIC POTENTIALS

Abstract

Starting from the one-dimensional Schrodinger equation with symmetric potential Vs(x), a general method is presented in order to obtain a family of partially isospectral hamiltonians. Arguments concerning supersymmetric transformations, factorization procedures and Riccati equations are invoked along the article. As a result of the appearance of singular superpotentials, the physical meaning of our method can be summarized as follows: only the odd wave-functions of the original potential Vs(x) are transported via supersymmetry into the Hilbert space associated with the partner Vp(x). In such a case the degeneracy of energy levels is partially broken. Supersymmetry is neither exact nor spontaneously broken but realizes itself acting on wave functions vanishing at x=0. While the domain of the original hamiltonian H extends along the whole real axis, the susy partner Hp reduces to the half-line (x≤0 or x≥0). To illustrate how the procedure works in practice we resort to a symmetric potential in the Posch-Teller class containing both discrete and continuous spectra.