Relativistic energy eigenvalues for the Dirac equation in the presence of vector and scalar potentials via the simple similarity transformation

Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = −A r + B1r and scalar S(r) = B2r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of...

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Bibliographic Details
Published in:Physica scripta 2012-12, Vol.86 (6), p.65005-5
Main Author: Barakat, T
Format: Article
Language:English
Subjects:
Dirac equation
Eigenvalues
Mathematical analysis
Scalars
Schroedinger equation
Similarity
Transformations
Vectors (mathematics)
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Summary:Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = −A r + B1r and scalar S(r) = B2r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = −A r, S(r) = B2r, and V (r) = 0, S(r) = B2r, respectively.
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/86/06/065005