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TMF, 2014, Volume 180, Number 3, Pages 342–367 (Mi tmf8582)  

This article is cited in 3 scientific papers (total in 3 papers)

The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential

V. V. Pupyshev

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

Abstract: We derive and qualitatively analyze nonlinear and linear equations for the scattering length and effective radius. We find and investigate exact solutions of these equations in the case of a centrally symmetric rectangular potential and elucidate a relation between the effective radius and the scattering length. We are especially interested in the cases of zero and unbounded scattering lengths.

Keywords: two-dimensional scattering, short-range potential, scattering length, effective radius

DOI: https://doi.org/10.4213/tmf8582

Full text: PDF file (663 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 180:3, 1051–1072

Bibliographic databases:

Received: 29.07.2013
Revised: 20.05.2014

Citation: V. V. Pupyshev, “The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential”, TMF, 180:3 (2014), 342–367; Theoret. and Math. Phys., 180:3 (2014), 1051–1072

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8582
  • http://mi.mathnet.ru/eng/tmf/v180/i3/p342

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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, “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
    2. 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
    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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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