This article is cited 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

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

DOI: 10.4213/tmf8583

 English version: Theoretical and Mathematical Physics, 2014, 179:1, 472–489

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