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

被引：0
作者：
V. V. Pupyshev
机构：
[1] Joint Institute for Nuclear Research,
来源：
Theoretical and Mathematical Physics | 2014年 / 179卷
关键词：
two-dimensional scattering; effective radius approximation; near-threshold resonance state; weakly bound state;
D O I：
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学科分类号：
摘要：
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.
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页码：472 / 489
页数：17
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