Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum

TL;DR

This paper adapts classicality analysis techniques to non-Hermitian quantum systems, specifically complex potentials with real spectra, revealing new insights into their pure states and classical-like properties.

Contribution

It introduces a method to study classicality in non-Hermitian systems, extending techniques from Hermitian quantum mechanics to complex-valued potentials with real spectra.

Findings

Classicality techniques can be adapted for non-Hermitian systems.

Complex potentials with real spectra exhibit classical-like properties.

The method applies to both PT-symmetric and non-PT-symmetric oscillators.

Abstract

We show that the standard techniques that are utilized to study the classical like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non-PT-symmetric and PT-symmetric oscillators exhibiting real spectra.