Hermitian and non-Hermitian formulations of the time evolution of quantum decay

TL;DR

This paper compares Hermitian and non-Hermitian approaches to quantum decay, demonstrating their equivalence for many potentials using Green's function analysis in the complex wave number plane.

Contribution

It shows that Hermitian and non-Hermitian formulations yield identical results for quantum decay in a broad class of potentials, using complex analysis techniques.

Findings

Both formulations produce identical descriptions for well-behaved potentials.

Analytical properties of Green's functions underpin the equivalence.

The approach applies to a large class of quantum decay problems.

Abstract

This work discusses Hermitian and non-Hermitian formulations for the time evolution of quantum decay, that involve respectively, continuum wave functions and resonant states, to show that they lead to an identical description for a large class of well behaved potentials. Our approach is based on the analytical properties of the outgoing Green's function to the problem in the complex wave number plane.