Geodesic
Energies of weakly bound and near-threshold resonance states of a~quantum particle in a~two-dimensional plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 102-122

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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. 
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     author = {V. V. Pupyshev},
     title = {Energies of weakly bound and near-threshold resonance states of a~quantum particle in a~two-dimensional plane},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {102--122},
     publisher = {mathdoc},
     volume = {179},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a6/}
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V. V. Pupyshev. Energies of weakly bound and near-threshold resonance states of a~quantum particle in a~two-dimensional plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 102-122. http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a6/