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Phase-integral solution of the radial Dirac equation
Högskolan Dalarna, Akademin Industri och samhälle, Fysik.ORCID-id: 0000-0002-5610-8323
2010 (Engelska)Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, nr 3, artikel-id 032304Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

A phase-integral (WKB) solution of the radial Dirac equation is constructed, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the classical transition points. The potential is allowed to be the time component of a four-vector, a Lorentz scalar, a pseudoscalar, or any combination of these. The key point in the construction is the transformation from two coupled first-order equations constituting the radial Dirac equation to a single second-order Schroumldinger-type equation. This transformation can be carried out in infinitely many ways, giving rise to different second-order equations but with the same spectrum. A unique transformation is found that produces a particularly simple second-order equation and correspondingly simple and well-behaved phase-integral solutions. The resulting phase-integral formulas are applied to unbound and bound states of the Coulomb potential. For bound states, the exact energy levels are reproduced.

Ort, förlag, år, upplaga, sidor
2010. Vol. 51, nr 3, artikel-id 032304
Nyckelord [en]
bound states; Dirac equation; integral equations; wave functions
Nationell ämneskategori
Naturvetenskap Fysik
Forskningsämne
Komplexa system - mikrodataanalys
Identifikatorer
URN: urn:nbn:se:du-10500DOI: 10.1063/1.3328454ISI: 000276210400010OAI: oai:DiVA.org:du-10500DiVA, id: diva2:542787
Tillgänglig från: 2012-08-03 Skapad: 2012-08-03 Senast uppdaterad: 2017-12-07Bibliografiskt granskad

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