Multichannel scattering for the Schrödinger equation on a line with different thresholds at both infinities

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-06 DOI:10.1098/rspa.2023.0847
Peter O. Kazinski, Petr S. Korolev
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Abstract

The multichannel scattering problem for the stationary Schrödinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the Jost solutions as functions of the spectral parameter is described. Unitarity of the scattering matrix is proved in the general case when some of the scattering channels can be closed and the thresholds can be different at left and right infinities on the line. The symmetry relations of the S-matrix are established. The condition determining the bound states is obtained. The asymptotics of the Jost functions and of the transition matrix are derived for a large spectral parameter.

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线性上薛定谔方程的多通道散射,两个无限点的阈值不同
研究了直线上静止薛定谔方程的多通道散射问题,该方程在两个无限点上具有不同的阈值。描述了约斯特解的分析结构以及与约斯特解相关的过渡矩阵作为谱参数函数的分析结构。在某些散射通道可能是封闭的,且线上左右无穷远处的阈值可能不同的一般情况下,证明了散射矩阵的单一性。建立了 S 矩阵的对称关系。得到了决定束缚态的条件。推导了大谱参数下乔斯特函数和过渡矩阵的渐近线。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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