斥势和强奇异相互作用的反向散射

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-08-12 DOI:10.1063/5.0215713

Atsuhide Ishida

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引用次数: 0

摘要

作者在 2014 年发表的一篇关于受斥力哈密顿支配的量子系统的论文中，证明了由规则和奇异部分组成的散射算子所描述的短程相互作用的唯一性。本文假定奇异部分具有更强的奇异性，并证明了相同的唯一性定理。通过应用恩斯和韦德发明的随时间变化的方法[J. Math. Phys. 36(8), 3902-3921 (1995)]，具有更强奇异性的散射算子的更宽类别的高速极限也唯一地确定了多维系统的相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Inverse scattering for repulsive potential and strong singular interactions

In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder [J. Math. Phys. 36(8), 3902–3921 (1995)], the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.