Closed formula for the metric in the Hilbert space of a PT-symmetric model

TL;DR

This paper presents an exactly solvable PT-symmetric non-Hermitian model with a real spectrum and derives a simple closed-form expression for its metric operator, connecting it to a Hermitian system.

Contribution

It introduces a new solvable PT-symmetric model and provides an explicit formula for its metric operator, advancing understanding of non-Hermitian quantum systems.

Findings

Derived a closed-form metric operator for the model

Confirmed the real spectrum of the PT-symmetric system

Established a link to a Hermitian counterpart

Abstract

We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.