du.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Publications (3 of 3) Show all publications
Thylwe, K.-E. & Linnaeus, S. (2011). Semiclassical aspects and supersymmetry of bound Dirac states for central pseudo-scalar potentials. Physica Scripta, 84(2), Article ID 025006.
Open this publication in new window or tab >>Semiclassical aspects and supersymmetry of bound Dirac states for central pseudo-scalar potentials
2011 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 84, no 2, article id 025006Article in journal (Refereed) Published
Abstract [en]

Relativistic bound states for a linear, radial pseudo-scalar potential model are discussed. The two radial Dirac components are known to have a close connection to partner states in super-symmetric quantum mechanical theory. The pseudo-scalar potential plays the role of the 'super potential'. Hence, the Dirac components satisfy decoupled Schrodinger-type equations with isospectral, so-called, 'partner potentials' except possibly for a single state; the ground state corresponding to one of the partner potentials. The energy spectrum of a confining linear radial potential is discussed in some detail. Accurate amplitude-phase computations and a novel semiclassical (phase-integral) approach are presented.

National Category
Physical Sciences
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-10429 (URN)10.1088/0031-8949/84/02/025006 (DOI)000294727900006 ()
Available from: 2012-08-03 Created: 2012-08-03 Last updated: 2017-12-07Bibliographically approved
diva2:542787
Open this publication in new window or tab >>Phase-integral solution of the radial Dirac equation
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.

Keywords
bound states; Dirac equation; integral equations; wave functions
National Category
Natural Sciences Physical Sciences
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-10500 (URN)10.1063/1.3328454 (DOI)000276210400010 ()
Available from: 2012-08-03 Created: 2012-08-03 Last updated: 2017-12-07Bibliographically approved
Linnaeus, S. (2005). Stokes constants for a singular wave equation. Journal of Mathematical Physics, 45(5), Article ID 053505.
Open this publication in new window or tab >>Stokes constants for a singular wave equation
2005 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 45, no 5, article id 053505Article in journal (Refereed) Published
Abstract [en]

The Stokes constants for arbitrary-order phase-integral approximations are calculated when the square of the wave number has either two simple zeros close to a second-order pole or one simple zero close to a first-order pole. The treatment is based on uniform approximations. All parameters may assume general complex values.

Keywords
phase-integral approximation, wave equation, Stokes constants
National Category
Physical Sciences
Identifiers
urn:nbn:se:du-1064 (URN)10.1063/1.1893213 (DOI)000229155700039 ()
Available from: 2005-05-12 Created: 2005-05-12 Last updated: 2017-12-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-5610-8323

Search in DiVA

Show all publications