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TMF, 2011, Volume 169, Number 3, Pages 368–390 (Mi tmf6736)  

This article is cited in 6 scientific papers (total in 6 papers)

Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions

V. R. Khalilov, K. E. Lee

Lomonosov Moscow State University, Moscow, Russia

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

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

Full text: PDF file (484 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 169:3, 1683–1703

Bibliographic databases:

Received: 08.12.2010
Revised: 09.03.2011

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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\by V.~R.~Khalilov, K.~E.~Lee
\paper Discrete spectra of the~Dirac Hamiltonian in Coulomb and Aharonov--Bohm potentials in $2+1$ dimensions
\jour TMF
\yr 2011
\vol 169
\issue 3
\pages 368--390
\mathnet{http://mi.mathnet.ru/tmf6736}
\crossref{https://doi.org/10.4213/tmf6736}
\transl
\jour Theoret. and Math. Phys.
\yr 2011
\vol 169
\issue 3
\pages 1683--1703
\crossref{https://doi.org/10.1007/s11232-011-0145-4}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  zmath  adsnasa  isi  elib  elib
    2. 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  crossref  mathscinet  isi  scopus
    3. 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  crossref  isi  scopus
    4. Khalilov V.R., Mamsurov I.V., “Planar Density of Vacuum Charge Induced By a Supercritical Coulomb Potential”, Phys. Lett. B, 769 (2017), 152–158  crossref  zmath  isi  scopus
    5. 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  crossref  isi  scopus
    6. 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  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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