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arXiv · 1601.03871

Detection Time Distribution for Several Quantum Particles

Roderich Tumulka
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Abstract

We address the question of how to compute the probability distribution of the time at which a detector clicks, in the situation of $n$ non-relativistic quantum particles in a volume $\Omega\subset \mathbb{R}^3$ in physical space and detectors placed along the boundary $\partial \Omega$ of $\Omega$. We have previously [arXiv:1601.03715] argued in favor of a rule for the 1-particle case that involves a Schr\"odinger equation with an absorbing boundary condition on $\partial \Omega$ introduced by Werner; we call this rule the "absorbing boundary rule." Here, we describe the natural extension of the absorbing boundary rule to the $n$-particle case. A key element of this extension is that, upon a detection event, the wave function gets collapsed by inserting the detected position, at the time of detection, into the wave function, thus yielding a wave function of $n-1$ particles. We also describe an extension of the absorbing boundary rule to the case of moving detectors.

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Roderich Tumulka. 2016-01-15. Detection Time Distribution for Several Quantum Particles. https://doi.org/10.1103/physreva.106.042220

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