Tuesday, June 19, 2012

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

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