Supersymmetric quantum mechanical generalized MIC-Kepler system

TL;DR

This paper constructs a supersymmetric extension of the generalized MIC-Kepler system, revealing two distinct spectral families based on Dirac quantization, and unifies them with an additional potential, also reproducing SUSY hydrogenic results.

Contribution

It introduces a SUSY framework for the generalized MIC-Kepler system, classifies systems into two families based on Dirac quantization, and unifies these families with an added potential.

Findings

Systems with half-integer  belong to a SUSY family with identical spectra except the ground state.

Systems with integer  form a separate SUSY family with similar spectral properties.

Adding an extra potential unifies the two families into a single SUSY system.

Abstract

We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition \mu= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same spectrum between the respective partner Hamiltonians except for the ground state. Similarly, the systems with integral Dirac quantization condition \mu =\pm 1,\pm 2, \pm 3,...... belong to another family. We show that, it is necessary to introduce additional potential to MIC-Kepler system in order to unify the two families into one. We also reproduce the results of the (super-symmetric) Hydrogenic problem in our study.