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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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