|
| related topics |
| {particle, mechanics, theory} |
| {time, wave, function} |
| {measurement, state, measurements} |
| {force, casimir, field} |
| {field, particle, equation} |
| {wave, scattering, interference} |
| {time, systems, information} |
| {equation, function, exp} |
| {cos, sin, state} |
|
Measurement as Absorption of Feynman Trajectories: Collapse of the Wave
Function Can be Avoided
A. Marchewka, Z. Schuss
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9906078
- categories:
- quant-ph
- comments:
- 20 pages, latex, no figures
- doi:
- 10.1103/PhysRevA.65.042112
- arxiv_id:
- quant-ph/9906078
- journal_ref:
- Phys.Rev.A65:042112,2002
- report_no:
- TAUP 2579/99
- created:
- 1999-06-21
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