Universal Forms for One-Dimensional Quantum Hamiltonians: A Comparison of the SUSY and the De La Peña Factorization Approaches

We show that by linking two factorization techniques often employed to solve Schroedinger’s equation one can give any one-dimensional hamiltonian the same form in terms of quantities typical of these approaches. These are the supersymmetric technique SUSY and the one of De La Peña’s. It is shown that the linkage between them exhibits interesting peculiarities, that are illustrated in the case of a very important family of quantum potentials, namely, reflection-less ones.