Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics

TL;DR

This paper explores non-Hermitian supersymmetric quantum mechanics applied to harmonic oscillators with centrifugal spikes, constructing creation and annihilation operators and analyzing their spectral properties and isospectrality.

Contribution

It introduces a formalism for non-Hermitian SUSY quantum mechanics that constructs creation and annihilation operators for complexified harmonic oscillators with unique spectral features.

Findings

Construction of creation and annihilation operators in non-Hermitian SUSY QM

Spectral analysis showing non-equidistant, yet isospectral, energy levels

Unusual degeneracy patterns in the spectrum

Abstract

Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct the factorized creation and annihilation operators. We show how the real though, generically, non-equidistant spectrum complies with the current SUSY-type isospectrality and degeneracy in an unusual way.