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Phase-integral solution of the radial Dirac equation
Dalarna University, School of Technology and Business Studies, Physics.ORCID iD: 0000-0002-5610-8323
2010 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 3, article id 032304Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2010. Vol. 51, no 3, article id 032304
Keywords [en]
bound states; Dirac equation; integral equations; wave functions
National Category
Natural Sciences Physical Sciences
Research subject
Komplexa system - mikrodataanalys
Identifiers
URN: urn:nbn:se:du-10500DOI: 10.1063/1.3328454ISI: 000276210400010OAI: oai:DiVA.org:du-10500DiVA, id: diva2:542787
Available from: 2012-08-03 Created: 2012-08-03 Last updated: 2017-12-07Bibliographically approved

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Linnaeus, Staffan

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  • de-DE
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  • nn-NB
  • sv-SE
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