球对称泡利哈密顿量的SUSY结构

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2025-05-18 DOI:10.1007/s00601-025-01994-w

Georg Junker

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引用次数: 0

摘要

结果表明，在外部球对称电磁势的影响下，表征非相对论性电子的量子哈密顿量表现出超对称结构。对球对称标量势和球对称矢量势进行了详细的讨论。目前的方法，包括自旋\(\frac{1}{2}\)自由度，为径向谐振子和库仑问题等已知模型提供了新的见解。我们还发现了一些新的精确可解模型，其中一个模型表现出一种新的混合类型的形状不变性，其中包含了势参数的平移和缩放。自旋轨道算符作为威滕宇称所起的基本作用得到了强调。

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On the SUSY Structure of Spherically Symmetric Pauli Hamiltonians

It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar potentials and spherical symmetric vector potentials are discussed in detail. The current approach, which includes the spin-\(\frac{1}{2}\) degree of freedom, provides new insights to known models like the radial harmonic oscillator and the Coulomb problem. We also find a few new exactly solvable models, one of them exhibiting a new mixed type of shape invariance containing translation and scaling of potential parameters. The fundamental role as Witten parity played by the spin-orbit operator is high-lighted.

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来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).