1206.3677 (Alexander Komech)

On Dynamical Justification of Quantum Scattering Cross Section    [PDF]

Alexander Komech

We give a dynamical justification of a differential cross section for the Schr\"odinger equation in the context of long time transition to stationary regime. Our approach is based on spherical incident waves, produced by a harmonic source, and uniform long-range asymptotics for the corresponding spherical limiting amplitudes. The main result is the convergence of the spherical limiting amplitudes to a limit as the source is moving to infinity. The main technical ingredients are the Agmon-Jensen-Kato analytical theory of the Green function and the Ikebe uniqueness theorem for the Lippmann-Schwinger equation.

View original: http://arxiv.org/abs/1206.3677