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

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