Factorization of supersymmetric Hamiltonians in curvilinear coordinates

TL;DR

This paper develops a general framework for supersymmetric quantum systems in curvilinear coordinates and explicitly constructs the SUSY extension of the Euler/Pauli Hamiltonian, connecting it to classical Coulomb problems in specific limits.

Contribution

It provides a comprehensive method for factorizing supersymmetric Hamiltonians in curvilinear coordinates and links the SUSY Coulomb problem to classical limits of a two-center system.

Findings

Constructed the SUSY extension of the Euler/Pauli Hamiltonian.

Connected SUSY Coulomb problem to limits of a two-center system.

Demonstrated separability in different coordinate systems.

Abstract

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.