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TMF, 2014, Volume 179, Number 1, Pages 102–122 (Mi tmf8583)  

This article is cited in 5 scientific papers (total in 5 papers)

Energies of weakly bound and near-threshold resonance states of a quantum particle in a two-dimensional plane

V. V. Pupyshev

Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We assume that a slow quantum particle moves in a two-dimensional plane of a three-dimensional coordinate space and its motion occurs in the field of a central short-range potential. We show that the approximate energies of weakly bound and near-threshold resonance states of this particle are defined by the roots of transcendental equations with two parameters: the scattering length and the effective radius. We find the sufficient conditions for solvability of these equations and study the dependence of their solutions on the parameters.

Keywords: two-dimensional scattering, effective radius approximation, near-threshold resonance state, weakly bound state

DOI: https://doi.org/10.4213/tmf8583

Full text: PDF file (643 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 179:1, 472–489

Bibliographic databases:

Received: 31.07.2013

Citation: V. V. Pupyshev, “Energies of weakly bound and near-threshold resonance states of a quantum particle in a two-dimensional plane”, TMF, 179:1 (2014), 102–122; Theoret. and Math. Phys., 179:1 (2014), 472–489

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8583
  • http://mi.mathnet.ru/eng/tmf/v179/i1/p102

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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. V. Pupyshev, “The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential”, Theoret. and Math. Phys., 180:3 (2014), 1051–1072  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. V. V. Pupyshev, “Effective-radius approximation in the problem of two-dimensional scattering by a central short-range potential”, Theoret. and Math. Phys., 182:2 (2015), 264–283  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions”, Theoret. and Math. Phys., 186:2 (2016), 213–230  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. V. V. Pupyshev, “The method of amplitude functions in two-dimensional scattering theory”, Theoret. and Math. Phys., 191:1 (2017), 499–523  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Belov P.A., “Energy Spectrum of Excitons in Square Quantum Wells”, Physica E, 112 (2019), 96–108  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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