### 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 language | English |
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Pages (from-to) | 6240-6253 |

Number of pages | 14 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 372 |

Issue number | 41 |

DOIs | |

Publication status | Published - 2008 Oct 6 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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**Trajectory interpretation of the uncertainty principle in 1D systems using complex Bohmian mechanics.** / Yang, Ciann-Dong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Trajectory interpretation of the uncertainty principle in 1D systems using complex Bohmian mechanics

AU - Yang, Ciann-Dong

PY - 2008/10/6

Y1 - 2008/10/6

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=51649091325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649091325&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2008.08.050

DO - 10.1016/j.physleta.2008.08.050

M3 - Article

VL - 372

SP - 6240

EP - 6253

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 41

ER -