Bohmian arrival time without trajectories

Sabine Kreidl, Gebhard Grübl and Hans G. Embacher

Institut für Theoretische Physik der Universität Innsbruck
Technikerstr. 25, A-6020 Innsbruck, Austria

Submitted May 27, 2003

Abstract. The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wave function tex2html_wrap_inline17 and its spatial derivative tex2html_wrap_inline19, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.

J. Phys. A: Math. Gen. 36, 8851 - 8865 (2003).

Preprint., 20 pages, 12 figures, 128 kB.