N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

TL;DR

This paper explores specific quantum mechanical models exhibiting N-fold supersymmetry at certain parameter values, analyzing their spectral properties and the distinction between quasi-exact and quasi-perturbative solvability.

Contribution

It provides a detailed analysis of N-fold supersymmetry in particular models, highlighting non-perturbative spectral features and the concept of dynamical supersymmetry breaking.

Findings

Identification of N-fold supersymmetry in periodic and sextic triple-well potentials

Observation of characteristic spectral features via valley method

Clarification of dynamical supersymmetry breaking mechanisms

Abstract

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.