On a Derivation of the Absorbing Boundary Rule

TL;DR

This paper explores a derivation of the absorbing boundary rule (ABR) for quantum particle detection, aiming to connect it with microscopic detector models, though the derivation remains non-rigorous.

Contribution

It provides a non-rigorous derivation of the ABR from known microscopic models, linking it to detector physics.

Findings

Outline of a derivation connecting ABR to microscopic models

Identification of known results used in the derivation

Highlighting the need for a rigorous proof

Abstract

Consider detectors waiting for a quantum particle to arrive at a surface $S$ in 3-space. For predicting the probability distribution of the time and place of detection, a rule was proposed in [arXiv:1601.03715], called the absorbing boundary rule (ABR) and involving a 1-particle Schr\"odinger equation with an absorbing boundary condition on $S$. While plausibility arguments for the ABR were given there, it would be desirable to derive the ABR from a microscopic model of a detector. We outline here such a derivation by putting together known results from the literature. Our derivation is non-rigorous, and it would still be desirable to have a rigorous version of it in the future.