International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 575217, 11 pages
doi:10.1155/2009/575217
Universal forms for one-dimensional quantum Hamiltonians: a comparison of the SUSY and the de la Peña factorization approaches
L. Canderle1
, A. Plastino2
, M. Casas3
and A.R. Plastino2
1Department of Physics, National University of La Pampa, La Pampa, Argentina
2National University of La Plata (UNLP), IFLP-CCT-CONICET C. C. 727, 1900 La Plata, Argentina
3Departament de Física, IFISC-CSIC, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
Abstract
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.