Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach

TL;DR

This paper presents a pathwise probabilistic approach to quantum scattering and flux theorems, providing intuitive interpretations and deriving quantum results through expectations of stochastic paths.

Contribution

It introduces a novel pathwise probabilistic framework for quantum scattering and flux theorems, connecting Nelson diffusions with quantum mechanics.

Findings

Pathwise probabilistic versions of scattering and flux theorems

Quantum results recovered via expectations of stochastic paths

Utilizes results by Carlen on Nelson diffusion paths

Abstract

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The quantum mechanical results can be then recovered by taking expectations in our pathwise statements.