A microscopic derivation of the quantum mechanical formal scattering cross section

Abstract

We prove that the empirical distribution of crossings of a "detector'' surface by scattered particles converges in appropriate limits to the scattering cross section computed by stationary scattering theory. Our result, which is based on Bohmian mechanics and the flux-across-surfaces theorem, is the first derivation of the cross section starting from first microscopic principles.

28 pages, v2: Typos corrected, layout improved, v3: Typos corrected. Accepted for publication in Comm. Math. Phys