On the Quantum Mechanical Scattering Statistics of Many Particles

TL;DR

This paper presents a Bohmian analysis of many-particle quantum scattering, deriving the $S$-matrix probability in the large-distance limit, addressing the complexities of multiple particles arriving at different times.

Contribution

It introduces a straightforward Bohmian approach to analyze many-particle scattering, extending the understanding of $S$-matrix probabilities beyond single-particle scenarios.

Findings

Derives $S$-matrix probability from Bohmian mechanics for many particles.

Shows the limit of large distances yields the standard scattering probabilities.

Addresses the challenge of multiple particles arriving at different times.

Abstract

The probability of a quantum particle being detected in a given solid angle is determined by the $S$-matrix. The explanation of this fact in time dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the $S$-matrix probability emerges in the limit of large distances.