Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

TL;DR

This paper explores non-Hermitian quantum mechanics incorporating a minimal length, providing exact solutions for specific models, demonstrating real spectra, and explicitly constructing the metric operator, thus advancing understanding of such systems.

Contribution

It presents the first exact solutions for non-Hermitian models with minimal length uncertainty and explicitly constructs the metric operator, showing their pseudo-Hermiticity.

Findings

Both models have real spectra.

Models are $ ext{eta}$ pseudo-Hermitian.

Explicit metric operators are derived.

Abstract

We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $\eta$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.