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The Dirac oscillator with a Coulomb-like tensor potential

H Akcay

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We study the Dirac equation with a tensor potential which contains a term linear in r and a Coulomb-like term. The eigenstates and eigenvalues are obtained exactly. We found that the energy spectrum and the degeneracy of the levels depend on the alignment of spin with the orbital angular momentum. For parallel alignment, the second term in the potential makes no contribution to the energy levels.


PACS

03.65.Pm Relativistic wave equations

03.65.Ge Solutions of wave equations: bound states

02.10.Ud Linear algebra

03.65.Fd Algebraic methods

MSC

81R15 Operator algebra methods (See also 46Lxx, 81T05)

15A72 Vector and tensor algebra, theory of invariants (See also 13A50, 14L24)

15A18 Eigenvalues, singular values, and eigenvectors

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

33C55 Spherical harmonics

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 24 (15 June 2007)

Received 1 February 2007, in final form 7 May 2007

Published 30 May 2007



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