# Flux-across-surfaces theorem for a Dirac particle

Published

Journal Article

We consider the asymptotic evolution of a relativistic spin-1/2 particle, i.e., a particle whose wave function 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 nonrelativistic results, known as flux across surfaces theorems, to the relativistic regime. © 2003 American Institute of Physics.

### Full Text

### Duke Authors

### Cited Authors

- Dürr, D; Pickl, P

### Published Date

- February 1, 2003

### Published In

### Volume / Issue

- 44 / 2

### Start / End Page

- 423 - 465

### International Standard Serial Number (ISSN)

- 0022-2488

### Digital Object Identifier (DOI)

- 10.1063/1.1528276

### Citation Source

- Scopus