D. Duerr, P. Pickl
Published 2002-07-05, updated 2002-09-23Version 2
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.
Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals
Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source
Transmission resonances for a Dirac particle in a one-dimensional Hulthén potential
