Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 029, 14 pages      arXiv:1012.0808      https://doi.org/10.3842/SIGMA.2011.029
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

Supersymmetry Transformations for Delta Potentials

David J. Fernández C. a, Manuel Gadella b and Luis Miguel Nieto b
a) Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico
b) Departamento de Física Teórica, Atómica y Optica, Facultad de Ciencias, 47041 Valladolid, Spain

Received November 30, 2010, in final form March 19, 2011; Published online March 22, 2011

Abstract
We make a detailed study of the first and second-order SUSY partners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the second-order transformations increase the spectral manipulation possibilities offered by the standard first-order supersymmetric quantum mechanics.

Key words: first and second-order SUSY; singular potentials.

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