V. R. Khalilov, K. E. Lee, “Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions”, TMF, 169:3 (2011), 368–390; Theoret. and Math. Phys., 169:3 (2011), 1683

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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 169, Number 3, Pages 368–390
DOI: https://doi.org/10.4213/tmf6736 (Mi tmf6736)

This article is cited in 7 scientific papers (total in 7 papers)

Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in

2 + 1

$2+1$ dimensions

V. R. Khalilov, K. E. Lee

Lomonosov Moscow State University, Moscow, Russia

Full-text PDF (484 kB) Citations (7)

References:

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DOI: https://doi.org/10.4213/tmf6736

Abstract: 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, Coulomb potential in

$2+1$ dimensions, Aharonov–Bohm potential, spin.

Received: 08.12.2010
Revised: 09.03.2011

English version:
Theoretical and Mathematical Physics, 2011, Volume 169, Issue 3, Pages 1683–1703
DOI: https://doi.org/10.1007/s11232-011-0145-4

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. R. Khalilov, K. E. Lee, “Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in

$2+1$ dimensions”, TMF, 169:3 (2011), 368–390; Theoret. and Math. Phys., 169:3 (2011), 1683–1703

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6736

https://doi.org/10.4213/tmf6736

https://www.mathnet.ru/eng/tmf/v169/i3/p368

This publication is cited in the following 7 articles:

Breev A.I., Ferreira R., Gitman D.M., Voronov B.L., “Spectra of Electronic Excitations in Graphene Near Coulomb Impurities”, J. Exp. Theor. Phys., 130:5 (2020), 711–736
Khalilov V.R., “Quantum States of a Neutral Massive Fermion With An Anomalous Magnetic Moment in An External Electric Field”, Mosc. Univ. Phys. Bull., 73:3 (2018), 293–300
Khalilov V.R., “Quasi-Stationary States and Fermion Pair Creation From a Vacuum in Supercritical Coulomb Field”, Mod. Phys. Lett. A, 32:38 (2017), 1750200
Kuleshov V.M., Mur V.D., Fedotov A.M., Lozovik Yu.E., “Coulomb Problem For Z > Z(Cr) in Doped Graphene”, J. Exp. Theor. Phys., 125:6 (2017), 1144–1162
Khalilov V.R., Mamsurov I.V., “Planar Density of Vacuum Charge Induced By a Supercritical Coulomb Potential”, Phys. Lett. B, 769 (2017), 152–158
Kuleshov V.M., Mur V.D., Narozhny N.B., “Coulomb Problem For Graphene With Supercritical Impurity”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012044
V. R. Khalilov, “Zero-mass fermions in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions”, Theoret. and Math. Phys., 175:2 (2013), 637–654

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	678
Full-text PDF :	225
References:	119
First page:	15

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