ON THE FLUX-ACROSS-SURFACES THEOREM

The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that s urface at some time. We prove the free flux-across-surfaces theorem, w hich was conjectured by Combes, Newton and Shtokhamer (Phys. Rev. D. 1 1 (1975), 366), and which relates the integrated quantum flux to the u sual quantum mechanical formula for the cross-section. The integrated quantum flux is equal to the probability of outward crossings of surfa ces by Bohmian trajectories in the scattering regime.