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.
|Number of pages||14|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 2008 Oct 6|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)