Canonical quantum potential scattering theory

TL;DR

This paper introduces a novel canonical formalism for quantum potential scattering, simplifying calculations of scattering parameters and providing a new perspective by drawing an analogy with classical dynamics.

Contribution

It develops a new formalism using canonical methods to derive simple differential equations for scattering parameters, applicable to various scattering systems.

Findings

Simplified calculation of scattering length and effective range.

Application to atom-atom and neutron-nucleus scattering.

Potential extension to charged particle scattering.

Abstract

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear first-order differential equations for the low energy scattering parameters like scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.