Detection Time Distribution for Several Quantum Particles

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 Schrödinger 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.

17 pages LaTeX, no figures

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• Existence of Schrodinger Evolution with Absorbing Boundary Condition
• Space-time-symmetric extension of quantum mechanics: Interpretation and arrival-time predictions
• On a Derivation of the Absorbing Boundary Rule
• Detection Time Distribution for Dirac Particles
• Absorbing detectors meet scattering theory
• Non-Heisenbergian quantum mechanics
• Energy-Time Uncertainty Relation for Absorbing Boundaries
• Detection Time Distribution Predicted Using Absorbing Boundary Conditions and Imaginary Potentials
• A solution of the quantum time of arrival problem via mathematical probability theory