Scattering Wavefunctions for a Dirac Particle in a Central Potential
| Autor: | T.A Weber, C.L Hammer, D.M Fradkin |
|---|---|
| Rok vydání: | 1964 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics. 5:1645-1651 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.1931201 |
| Popis: | The scattering wavefunction for a Dirac particle in a central potential is written in terms of a matrix acting on a plane-wave spinor whose momentum direction p and polarization direction are the assigned directions for the asymptotic incident plane wave. The matrix involves four functions, independent of polarization direction, which multiply the matrices 1, α·(p − r), α·(p + r), and p·r·σ. Differential relations for these four functions are directly obtained and asymptotic relations are given. In particular, the function multiplying α·(p + r) is asymptotically zero, so the potential scattering formulation is identical with that given previously for the Coulomb potential. The scattering wavefunction is a solution of the general differential relations subject to appropriate boundary conditions. For the Coulomb potential, these differential relations simplify, and an iterative solution is developed based on a Green's function technique with the Sommerfeld-Maue approximation as the zero-order solution. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|