The non-Hermitian Swanson model with a time-dependent metric

TL;DR

This paper extends solutions to the time-dependent Dyson and quasi-Hermiticity relations for a generalized non-Hermitian Swanson Hamiltonian, employing the Lewis-Riesenfeld method to find physical solutions with potential applications.

Contribution

It provides new solutions to time-dependent non-Hermitian Hamiltonians using the Lewis-Riesenfeld invariant method, specifically for a generalized non-Hermitian Swanson model.

Findings

Constructed explicit time-dependent solutions for the generalized non-Hermitian Swanson Hamiltonian.

Demonstrated physical applications of the solutions in quantum systems.

Extended the theoretical framework for time-dependent non-Hermitian quantum mechanics.

Abstract

We provide further non-trivial solutions to the recently proposed time-dependent Dyson and quasi-Hermiticity relation. Here we solve them for the generalized version of the non-Hermitian Swanson Hamiltonian with time-dependent coefficients. We construct time-dependent solutions by employing the Lewis-Riesenfeld method of invariants and discuss concrete physical applications of our results.