International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 575217, 11 pages
Universal Forms for One-Dimensional Quantum Hamiltonians: A Comparison of the SUSY and the De La Peña Factorization Approaches
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
4Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
Received 6 May 2009; Revised 28 June 2009; Accepted 24 August 2009
Academic Editor: Roger Grimshaw
Copyright © 2009 L. Canderle et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.