Trajectory interpretation of the uncertainty principle in 1D systems using complex Bohmian mechanics

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Abstract

Complex Bohmian mechanics is introduced to investigate the validity of a trajectory interpretation of the uncertainty principles Δ q Δ p ≥ ℏ / 2 and Δ E Δ t ≥ ℏ / 2 by replacing probability mean values with time-averaged mean values. It is found that the ℏ / 2 factor in the uncertainty relation Δ E Δ t ≥ ℏ / 2 stems from a quantum potential whose time-averaged mean value taken along any closed trajectory with a period T = 2 π / ω is proved to be an integer multiple of ℏ ω / 2 for one-dimensional systems.

Original languageEnglish
Pages (from-to)6240-6253
Number of pages14
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume372
Issue number41
DOIs
Publication statusPublished - 2008 Oct 6

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complex systems
trajectories
stems
integers

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Trajectory interpretation of the uncertainty principle in 1D systems using complex Bohmian mechanics",
abstract = "Complex Bohmian mechanics is introduced to investigate the validity of a trajectory interpretation of the uncertainty principles Δ q Δ p ≥ ℏ / 2 and Δ E Δ t ≥ ℏ / 2 by replacing probability mean values with time-averaged mean values. It is found that the ℏ / 2 factor in the uncertainty relation Δ E Δ t ≥ ℏ / 2 stems from a quantum potential whose time-averaged mean value taken along any closed trajectory with a period T = 2 π / ω is proved to be an integer multiple of ℏ ω / 2 for one-dimensional systems.",
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AB - Complex Bohmian mechanics is introduced to investigate the validity of a trajectory interpretation of the uncertainty principles Δ q Δ p ≥ ℏ / 2 and Δ E Δ t ≥ ℏ / 2 by replacing probability mean values with time-averaged mean values. It is found that the ℏ / 2 factor in the uncertainty relation Δ E Δ t ≥ ℏ / 2 stems from a quantum potential whose time-averaged mean value taken along any closed trajectory with a period T = 2 π / ω is proved to be an integer multiple of ℏ ω / 2 for one-dimensional systems.

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