N-fold Supersymmetry in Quantum Mechanical Matrix Models

TL;DR

This paper extends N-fold supersymmetry to quantum mechanical matrix models, constructing specific 2x2 systems that are weakly quasi-solvable and highlighting novel inequivalent cases.

Contribution

It introduces N-fold supersymmetry in matrix models and constructs new 2x2 Hermitian systems with unique properties not reducible to scalar cases.

Findings

Two inequivalent 2x2 supersymmetric systems constructed

Both systems characterized by two arbitrary scalar functions

Systems are weakly quasi-solvable

Abstract

We formulate N-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix 2-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems, both of which are characterized by two arbitrary scalar functions, and one of which does not reduce to the scalar system. The obtained systems are all weakly quasi-solvable.