A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models

TL;DR

This paper introduces a generalized non-Hermitian oscillator Hamiltonian with explicit PT-symmetry breaking, transforms it into an equivalent Hermitian form, and explores N-fold supersymmetry in position-dependent mass models.

Contribution

It presents a new generalized non-Hermitian oscillator Hamiltonian with linear terms, and establishes the criterion for N-fold supersymmetry in position-dependent mass systems.

Findings

Hamiltonian can be transformed into an equivalent Hermitian form

N-fold supersymmetry criterion is applicable to the model

Explicit PT-symmetry breaking is incorporated into the Hamiltonian

Abstract

A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PT-symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the criterion of N-fold supersymmetry with a position-dependent mass is shown to reside in it.