ar X iv : m at h - ph / 0 20 70 10 v 2 2 3 Se p 20 02 Flux - Across - Surfaces Theorem for a Dirac Particle
نویسندگان
چکیده
We consider the asymptotic evolution of a relativistic spin-1 2 particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability , that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime.
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ar X iv : m at h - ph / 0 40 80 14 v 2 1 3 Ja n 20 06 The Flux - Across - Surfaces Theorem under conditions on the scattering state
The flux-across-surfaces theorem (FAST) describes the outgoing asymptotics of the quantum flux density of a scattering state. The FAST has been proven for potential scattering under conditions on the outgoing asymptote ψout (and of course under suitable conditions on the scattering potential). In this article we prove the FAST under conditions on the scattering state itself. In the proof we wil...
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