Geodesic
Discrete spectra of the~Dirac Hamiltonian in Coulomb and Aharonov--Bohm potentials in $2+1$ dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 3, pp. 368-390

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We find all self-adjoint Dirac Hamiltonians in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions with the fermion spin taken into account. We obtain implicit equations for the spectra and construct eigenfunctions for all self-adjoint Dirac Hamiltonians in the indicated external fields. We find explicit solutions of the equations for the spectra in some cases.
Keywords: symmetric operator, self-adjoint extension of the Hamiltonian, Aharonov–Bohm potential, spin.
Mots-clés : Coulomb potential in $2+1$ dimensions 
@article{TMF_2011_169_3_a3,
     author = {V. R. Khalilov and K. E. Lee},
     title = {Discrete spectra of {the~Dirac} {Hamiltonian} in {Coulomb} and {Aharonov--Bohm} potentials in $2+1$ dimensions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {368--390},
     publisher = {mathdoc},
     volume = {169},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_3_a3/}
}
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V. R. Khalilov; K. E. Lee. Discrete spectra of the~Dirac Hamiltonian in Coulomb and Aharonov--Bohm potentials in $2+1$ dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 3, pp. 368-390. http://geodesic.mathdoc.fr/item/TMF_2011_169_3_a3/