1202.2457 (M. A. Gonzalez Leon et al.)

Factorization of supersymmetric Hamiltonians in curvilinear coordinates    [PDF]

M. A. Gonzalez Leon, J. Mateos Guilarte, M. de la Torre Mayado

Planar supersymmetric quantum mechanical systems with separable spectral
problem in curvilinear coordinates are analyzed in full generality. We
explicitly construct the supersymmetric extension of the Euler/Pauli
Hamiltonian describing the motion of a light particle in the field of two heavy
fixed Coulombian centers. We shall also show how the SUSY Kepler/Coulomb
problem arises in two different limits of this problem: either, the two centers
collapse in one center - a problem separable in polar coordinates -, or, one of
the two centers flies to infinity - to meet the Coulomb problem separable in
parabolic coordinates.

View original: http://arxiv.org/abs/1202.2457