sl(2) Construction of Type A N-fold supersymmetry

TL;DR

This paper demonstrates that Type A N-fold supersymmetry in one-dimensional quantum mechanics can be constructed using sl(2) algebra, leading to less restrictive conditions and insights into quasi-solvability of certain models.

Contribution

It introduces a new sl(2)-based construction method for Type A N-fold supersymmetry, expanding the understanding of quasi-solvable quantum systems.

Findings

Constructed Type A N-fold supersymmetry using sl(2) algebra.

Derived a less restrictive condition for Type A N-fold supersymmetry.

Analyzed known models within this new construction framework.

Abstract

N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eigenvalues can be obtained for a portion of the spectra. We show that recently found Type A N-fold supersymmetry can be constructed by using sl(2) algebra, which provides a basis for the quasi-solvability. By this construction we find a condition for the Type A N-fold supersymmetry, which is less restrictive than the condition known previously. Several explicitly known models are also examined in the light of this construction.