Detection Time Distribution for Several Quantum Particles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866917833990995968 |
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| author | Tumulka, Roderich |
| author_facet | Tumulka, Roderich |
| contents | 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 $Ω\subset \mathbb{R}^3$ in physical space and detectors placed along the boundary $\partial Ω$ of $Ω$. 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 $\partial Ω$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_03871 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Detection Time Distribution for Several Quantum Particles Tumulka, Roderich Quantum Physics 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 $Ω\subset \mathbb{R}^3$ in physical space and detectors placed along the boundary $\partial Ω$ of $Ω$. 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 $\partial Ω$ 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. |
| title | Detection Time Distribution for Several Quantum Particles |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/1601.03871 |