Non-Hermitian time-dependent quantum systems with real energies

TL;DR

This paper investigates a class of non-Hermitian, time-dependent quantum systems with real energies, providing explicit solutions for wave-functions and propagators, relevant for quantum optics and chemistry.

Contribution

It introduces explicit solutions for wave-functions and propagators in non-Hermitian, time-dependent quantum systems with real energies, expanding understanding of such systems.

Findings

Wave-functions and propagators derived explicitly.

Systems exhibit real energy values despite non-Hermiticity.

Applicable to quantum optics and chemistry models.

Abstract

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum chemistry, which consists of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. The propagator for a general time-dependence of the parameters and the wave-functions are obtained explicitly for constant frequency and mass and a linear time-dependence in the potential. The wave-functions are used to obtain the expectation value of the Hamiltonian. Although it is neither Hermitian nor PT symmetric, the case under study exhibits real values of energy.