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??/2 and ΔEΔt??/2 by replacing probability mean values with time-averaged mean values. It is found that the ?/2 factor in the uncertainty relation ΔEΔt??/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 ?ω/2 for one-dimensional systems.