One-Dimensional Scattering Theory

Roger G. Newton

Willi-Hans Steeb

Wen-Du Li, Wu-Sheng Dai

Abstract In conventional scattering theory, by large-distance asymptotics, at the cost of losing the information of the distance between target and observer, one imposes large-distance asymptotics to achieve a scattering wave function which can be represented explicitly by a scattering phase shift. In this paper, without large-distance asymptotics, we establish an arbitrary-dimensional scattering theory. Arbitrary-dimensional scattering wave functions, scattering boundary conditions, and phase shifts are given without large-distance asymptotics. We give a discussion of one- and two-dimensional scatterings. Moreover, we also suggest a dimensional renormalization scheme to remove the divergence encountered in singular-potential scattering.

Jingfeng Liu, Ming Zhou, Zongfu Yu

A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.

Charles G. Wohl

Tapan Kumar Das