New supersymmetry-generated complex potentials with real spectra

TL;DR

This paper introduces a novel method to construct complex supersymmetric potentials with real spectra using the Ermakov equation, leading to new PT-symmetric and regular quantum systems with potential applications.

Contribution

It presents a new approach to generate complex superpotentials with real spectra based on the Ermakov equation, expanding the class of solvable non-Hermitian quantum models.

Findings

Constructed complex potentials with real spectra using Ermakov parameters.

Developed PT-symmetric and regular supersymmetric partner potentials.

Introduced a family of complex oscillators with real frequencies and spectra.

Abstract

A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation of the Schroedinger type. The superpotentials so constructed are characterized by the Ermakov parameters in such a way that they are always complex-valued and lead to non-Hermitian Hamiltonians with real spectra, whose eigenfunctions form a bi-orthogonal system. As applications we present new complex supersymmetric partners of the free particle that are PT-symmetric and can be either periodic or regular (of the Poeschl-Teller form). A new family of complex oscillators with real frequencies that have the energies of the harmonic oscillator plus an additional real eigenvalue is introduced.