Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry

TL;DR

This paper derives the metric operator for a specific non-Hermitian Hamiltonian and explores its pseudo-supersymmetric structure, providing new tools for analyzing such quantum systems.

Contribution

It introduces a method to construct the metric operator for a non-Hermitian Hamiltonian and establishes the connection to pseudo-supersymmetry in a specific potential model.

Findings

Derived the metric operator $ heta=exp T$ for the Hamiltonian

Found the intertwining operator linking the Hamiltonian to its pseudo-supersymmetric partner

Applied the framework to the hyperbolic Rosen-Morse II potential

Abstract

We have obtained the metric operator $\Theta=\exp T$ for the non-Hermitian Hamiltonian model $H=\omega(a^{\dag}a+1/2)+\alpha(a^{2}-a^{\dag^{2}})$. We have also found the intertwining operator which connects the Hamiltonian to the adjoint of its pseudo-supersymmetric partner Hamiltonian for the model of hyperbolic Rosen-Morse II potential.