Solutions of time-dependent Schrodinger equations for model non-Hermitian quantum mechanical systems

TL;DR

This paper solves the time-dependent Schrödinger equation for non-Hermitian quantum models, revealing unique spectral properties and behaviors in confined and unconfined systems, including defective matrices and complex energies.

Contribution

It provides new solutions and insights into non-Hermitian quantum systems, especially regarding eigenvalue patterns and the effects of confinement.

Findings

Eigenvalue energies differ between confined and unconfined systems.

Defective matrices lead to non-observable energies.

Complex energies are characteristic of non-Hermitian models.

Abstract

The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and situations where the matrix is defective. In addition the stationary states for infinite dimensional model system, which is confined in space , is examined and it is shown that the pattern of eigenvalue energies differs from when the system is unconfined.