Real discrete spectrum in the complex non-PT-symmetric Scarf II potential

TL;DR

This paper discovers new parameter regions in a complex, non-PT-symmetric Scarf II potential where the Hamiltonian has a real, discrete spectrum, expanding understanding beyond PT-symmetric cases.

Contribution

It identifies novel non-PT-symmetric parametric domains with real spectra and discusses their pseudo-Hermitian properties, which were previously unexplored.

Findings

New non-PT-symmetric domains with real discrete spectra

Potential pseudo-Hermiticity of the Hamiltonian in these domains

Extension of spectral properties beyond PT-symmetric cases

Abstract

Hitherto, it is well known that complex PT-symmetric Scarf II has real discrete spectrum in the parametric domain of unbroken PT-symmetry. We reveal new interesting complex, non-PT-symmetric parametric domains of this versatile potential, $V(x)$, where the spectrum is again discrete and real. Showing that the Hamiltonian, $p^2/2m+V(x)$, in the new cases is pseudo-Hermitian could be challenging, if possible.