Exact solution for the time dependent non-Hermitian generalized Swanson oscillator

TL;DR

This paper provides an exact analytical solution to the time-dependent non-Hermitian generalized Swanson oscillator, transforming it into a solvable time-independent harmonic oscillator through specific parameter choices.

Contribution

It introduces a method to solve the non-Hermitian time-dependent oscillator exactly by applying transformations and parameter tuning.

Findings

Exact solutions for the non-Hermitian oscillator are obtained.

The model reduces to a standard harmonic oscillator under certain conditions.

The approach can be applied to similar non-Hermitian systems.

Abstract

We produce an exact solution of the Schr\"odinger equation for the generalized time dependent Swanson oscillator. The system studied is a non-Hermitian setup characterized by time dependent complex coefficients. The exact solution is obtained by applying two transformations and under the right choice of the relevant parameters. Consequently, the model is reduced to a time independent harmonic oscillator.