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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 1, Pages 102–122
DOI: https://doi.org/10.4213/tmf8583 (Mi tmf8583) 		 
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (643 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf8583
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.
Received: 31.07.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 1, Pages 472–489
DOI: https://doi.org/10.1007/s11232-014-0156-z
Bibliographic databases:
Document Type: Article
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/tmf8583
  • https://doi.org/10.4213/tmf8583
  • https://www.mathnet.ru/eng/tmf/v179/i1/p102
    • This publication is cited in the following 6 articles:
    1. V. V. Pupyshev, “Study of Two-Dimensional Low-Energy Scattering by the Variable Phase Approach”, Phys. Part. Nuclei Lett., 20:6 (2023), 1366  crossref
    2. P. A. Belov, “Energy spectrum of excitons in square quantum wells”, Physica E, 112 (2019), 96–108  crossref  isi
    3. 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
    4. 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  isi  elib
    5. 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
    6. 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  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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