dorsal/arxiv
View SchemaMeasurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided
| Authors | A. Marchewka, Z. Schuss |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906078 |
| URL | https://arxiv.org/abs/quant-ph/9906078 |
| DOI | 10.1103/PhysRevA.65.042112 |
| Journal | Phys.Rev.A65:042112,2002 |
Abstract
We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the absorbed particles leave on the detector is identifies as the absorption current density on the detector. This density is calculated from the solution of Schr\"odinger's equation with a reflecting boundary at the detector. This current density is not the usual Schr\"odinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of 4 postulates. We postulate, among others, that a quantum particle has a trajectory. In the resulting theory the quantum mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two examples are presented, that of the slit experiment and the slit experiment with absorbing boundaries to measure time of arrival. A calculation is given of the two dimensional probability density function of a free particle from the measurement of the absorption current on two planes.
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"abstract": "We define a measuring device (detector) of the coordinate of quantum particle\nas an absorbing wall that cuts off the particle\u0027s wave function. The wave\nfunction in the presence of such detector vanishes on the detector. The trace\nthe absorbed particles leave on the detector is identifies as the absorption\ncurrent density on the detector. This density is calculated from the solution\nof Schr\\\"odinger\u0027s equation with a reflecting boundary at the detector. This\ncurrent density is not the usual Schr\\\"odinger current density. We define the\nprobability distribution of the time of arrival to a detector in terms of the\nabsorption current density. We define coordinate measurement by an absorbing\nwall in terms of 4 postulates. We postulate, among others, that a quantum\nparticle has a trajectory. In the resulting theory the quantum mechanical\ncollapse of the wave function is replaced with the usual collapse of the\nprobability distribution after observation. Two examples are presented, that of\nthe slit experiment and the slit experiment with absorbing boundaries to\nmeasure time of arrival. A calculation is given of the two dimensional\nprobability density function of a free particle from the measurement of the\nabsorption current on two planes.",
"arxiv_id": "quant-ph/9906078",
"authors": [
"A. Marchewka",
"Z. Schuss"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.042112",
"journal_ref": "Phys.Rev.A65:042112,2002",
"title": "Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided",
"url": "https://arxiv.org/abs/quant-ph/9906078"
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