Simultaneous Type A N-fold Supersymmetry with Two Different Values of N

TL;DR

This paper explores quantum systems with simultaneous type A N-fold supersymmetry at two different N values, identifying four distinct models with unique mathematical properties including conformal, hyperbolic, and elliptic types.

Contribution

It introduces the concept of systems exhibiting dual N-fold supersymmetry and classifies four inequivalent models with different geometric characteristics.

Findings

Identified four inequivalent models with dual N-fold supersymmetry.

Classified models into conformal, hyperbolic, and elliptic types.

Demonstrated the existence of models with two different N values simultaneously.

Abstract

We investigate one-dimensional quantum mechanical systems which have type A N-fold supersymmetry with two different values of N simultaneously. We find that there are essentially four inequivalent models possessing the property, one is conformal, two of them are hyperbolic (trigonometric) including Rosen-Morse type, and the other is elliptic.