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Simple proof for global existence of bohmian trajectories
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UNSPECIFIED (2005) Simple proof for global existence of bohmian trajectories. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 258 (2). pp. 349-365. doi:10.1007/s00220-005-1302-0 ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-005-1302-0
Abstract
We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wave-function obeying either the Schrodinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is ill-defined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide an alternative proof of the known global existence result for spinless Schrodinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result is conditions on the current vector field on configuration-space-time which are sufficient for almost-sure global existence.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QC Physics | ||||
| Journal or Publication Title: | COMMUNICATIONS IN MATHEMATICAL PHYSICS | ||||
| Publisher: | SPRINGER | ||||
| ISSN: | 0010-3616 | ||||
| Official Date: | September 2005 | ||||
| Dates: |
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| Volume: | 258 | ||||
| Number: | 2 | ||||
| Number of Pages: | 17 | ||||
| Page Range: | pp. 349-365 | ||||
| DOI: | 10.1007/s00220-005-1302-0 | ||||
| Publication Status: | Published |
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