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

SIGMA 3 (2007), 124, 24 pages      arXiv:0712.3682      https://doi.org/10.3842/SIGMA.2007.124
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

M.A. González León a, J. Mateos Guilarte b and M. de la Torre Mayado b
a) Departamento de Matemática Aplicada, Universidad de Salamanca, Spain
b) Departamento de Física Fundamental, Universidad de Salamanca, Spain

Received October 09, 2007, in final form December 10, 2007; Published online December 21, 2007

Abstract
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.

Key words: supersymmetry; integrability; quantum mechanics; two Coulombian centers.

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