Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures

TL;DR

This paper develops exact solutions for time-dependent non-Hermitian oscillators, linking classical and quantum models, and generalizes the Swanson oscillator to include the Caldirola-Kanai model, demonstrating real spectra and parameter-dependent Hermitian limits.

Contribution

It introduces a method to solve time-dependent non-Hermitian oscillators exactly, extending the Swanson oscillator to a broader class including the Caldirola-Kanai model.

Findings

All systems have real spectra.

Explicit classical and quantum solutions are provided.

Systems transition to Hermitian form for specific parameters.

Abstract

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola-Kanai model as a particular case. Explicit solutions are given in both, the classical and quantum pictures.