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TMF, 2010, Volume 163, Number 1, Pages 132–139 (Mi tmf6491)  

This article is cited in 8 scientific papers (total in 8 papers)

Fermion bound states in the Aharonov–Bohm field in $2+1$ dimensions

V. R. Khalilov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We find exact solutions of the Dirac equation that describe fermion bound states in the Aharonov–Bohm potential in $2+1$ dimensions with the particle spin taken into account. For this, we construct self-adjoint extensions of the Hamiltonian of the Dirac equation in the Aharonov–Bohm potential in $2+1$ dimensions. The self-adjoint extensions depend on a single parameter. We select the range of this parameter in which quantum fermion states are bound. We demonstrate that the energy levels of particles and antiparticles intersect. Because solutions of the Dirac equation in the Aharonov–Bohm potential in $2+1$ dimensions describe the behavior of relativistic fermions in the field of the cosmic string in $3+1$ dimensions, our results can presumably be used to describe fermions in the cosmic string field.

Keywords: spin, Aharonov–Bohm potential, symmetric operator, self-adjoint Hamiltonian, bound state, level intersection

DOI: https://doi.org/10.4213/tmf6491

Full text: PDF file (354 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 163:1, 511–516

Bibliographic databases:

Received: 10.09.2009

Citation: V. R. Khalilov, “Fermion bound states in the Aharonov–Bohm field in $2+1$ dimensions”, TMF, 163:1 (2010), 132–139; Theoret. and Math. Phys., 163:1 (2010), 511–516

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v163/i1/p132

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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. Khalilov V.R., Lee K.E., “Planar massless fermions in Coulomb and Aharonov-Bohm potentials”, Internat. J. Modern Phys. A, 27:29 (2012), 1250169, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. 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
    3. Khalilov V.R., “Creation of Planar Charged Fermions in Coulomb and Aharonov-Bohm Potentials”, Eur. Phys. J. C, 73:8 (2013), 2548  crossref  adsnasa  isi  scopus
    4. V. R. Khalilov, “Bound states of massive fermions in Aharonov–Bohm-like fields”, Eur. Phys. J. C, 74:1 (2014), 2708, 7 pp.  crossref  adsnasa  isi  scopus
    5. Silva E.O., “On Planar Quantum Dynamics of a Magnetic Dipole Moment in the Presence of Electric and Magnetic Fields”, Eur. Phys. J. C, 74:10 (2014), 3112  crossref  isi  scopus
    6. Azevedo F.S., Silva E.O., Castro L.B., Filgueiras C., Cogollo D., “Relativistic Quantum Dynamics of a Neutral Particle in External Electric Fields: An Approach on Effects of Spin”, Ann. Phys., 362 (2015), 196–207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Khalilov V.R., “Quantum States of a Neutral Massive Fermion With An Anomalous Magnetic Moment in An Aharonov-Casher Field”, Int. J. Mod. Phys. A, 32:18 (2017), 1750111  crossref  zmath  isi  scopus
    8. 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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