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.

arXiv comment28 pages, v2: Typos corrected, layout improved, v3: Typos corrected. Accepted for publication in Comm. Math. Phys

References in corpus (6)

• Quantum Equilibrium and the Origin of Absolute Uncertainty
• On the Global Existence of Bohmian Mechanics
• Simple Proof for Global Existence of Bohmian Trajectories
• Scattering theory from microscopic first principles
• Flux-Across-Surfaces Theorem for a Dirac Particle
• The Flux-Across-Surfaces Theorem under conditions on the scattering state

Cited by in corpus (2)

• Bohmian Mechanics and Quantum Information
• Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times