Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem

Details Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem

1994-05-02

arxiv.org/abs/hep-th/9405009v1

Phys. Rev. D, 50 (1994) 7715

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1103/PhysRevD.50.7715

The spin-1/2 Aharonov-Bohm problem is examined in the Galilean limit for the case in which a Coulomb potential is included. It is found that the application of the self-adjoint extension method to this system yields singular solutions only for one-half the full range of flux parameter which is allowed in the limit of vanishing Coulomb potential. Thus one has a remarkable example of a case in which the condition of normalizability is necessary but not sufficient for the occurrence of singular solutions. Expressions for the bound state energies are derived. Also the conditions for the occurrence of singular solutions are obtained when the non-gauge potential is $\xi/r^p (0\leq p<2)$.

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