Scattering theory using smeared non-Hermitian potentials

TL;DR

This paper develops a modified scattering theory framework for slightly non-local, non-Hermitian potentials, ensuring causality, unitarity, and asymptotic Hermiticity in quantum scattering processes.

Contribution

It introduces a new approach to scattering theory that accommodates non-local, non-Hermitian potentials while preserving fundamental physical principles.

Findings

Established a causal and unitary scattering theory for non-Hermitian potentials.

Demonstrated the feasibility of using smeared, non-Hermitian potentials in scattering.

Revealed conditions under which non-Hermitian potentials can be incorporated into standard scattering frameworks.

Abstract

Complex, non-Hermitian potentials V(x) can often generate standard quantum bound states. H. F. Jones [Phys. Rev. D 78, 065032 (2008)] demonstrated that the idea cannot directly be transferred to scattering. We reveal that a return to the causal and unitary and asymptotically Hermitian scattering theory exists for potentials which are allowed slightly non-local, V=V(x,p).