自旋正则化发生器和氢原子对称代数的相干分布

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:10.1063/5.0172309
E. M. Novikova
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引用次数: 0

摘要

本文提出了一种解决连续谱算子谱问题的新方法,即利用相干施瓦茨分布对问题进行积分变换。所构建的相干分布族是普通相干态族的完整类比。更确切地说,它满足普通相干态所满足的所有 Gazeau-Klauder 公理。但与属于湮没算子(或算子)点谱的相干态不同,相干分布属于某些赫米特算子的连续谱。因此,相干分布比相干态更适合作为连续谱算子广义特征函数积分表示的内核。在这项工作中,我们以解决量子力学的一个基本问题,即氢原子哈密顿频谱的连续部分问题为例,证明了这种方法。
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Coherent distributions of the symmetry algebra of spinor regularization generator and hydrogen atom
A new approach is developed for solving spectral problems for operators with continuous spectrum, which consists in the integral transform of the problem by using coherent Schwartz distributions. The constructed family of coherent distributions is a complete analogue of the family of ordinary coherent states. More precisely, it satisfies all Gazeau–Klauder axioms satisfied by the usual coherent states. But in contrast to the coherent states belonging to the point spectrum of the annihilation operator (or operators), the coherent distributions belong to the continuous spectrum of some Hermitian operators. Therefore, the coherent distributions work better than the coherent states as the kernel of the integral representation of generalized eigenfunctions of operators with continuous spectrum. In this work, this approach is demonstrated with an example of solving a basic problem of quantum mechanics, i.e., the problem of the continuous part of the spectrum of the Hamiltonian of the hydrogen atom.
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来源期刊
Journal of Mathematical Physics
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.
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