González León, M.A.; Mateos Guilarte, J.; de la Torre Mayado, M.

Two-dimensional supersymmetric quantum mechanics: two fixed centers of force

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 124, 24 p., electronic only (2007)


Summary: 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.

Mathematics Subject Classification

81Q60, 81V55


supersymmetry, integrability, quantum mechanics, two Coulombian centers