Integral Equation Approach for a Hydrogen Atom in a Strong Magnetic Field

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Few-Body Systems Pub Date : 2024-10-26 DOI:10.1007/s00601-024-01969-3

B. P. Carter, Z. Papp

引用次数: 0

Abstract

The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwinger form. Then, we approximate the asymptotically irrelevant parts by a discrete Hilbert space basis that allows an exact analytic evaluation of the relevant Green’s operators by continued fractions. The total asymptotic Green’s operator is calculated by a complex contour integral of subsystem Green’s operators. We present a sample of numerical results for a wide range of magnetic field strengths.

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强磁场中氢原子的积分方程法

氢原子在强磁场中的问题是量子系统在不同方向上具有真正不同渐近行为的一个臭名昭著的例子。在垂直于磁场的方向上，运动是二次受限的，而在沿着磁场线的方向上，运动则是库仑扭曲的自由运动。在这项工作中，我们确定了哈密顿的渐近相关部分，并将问题转化为李普曼-施文格形式。然后，我们用离散的希尔伯特空间基础来近似渐近相关部分，这样就可以用续分数对相关的格林算子进行精确的分析评估。总的渐近格林算子是通过子系统格林算子的复等值线积分计算出来的。我们展示了各种磁场强度下的数值结果样本。

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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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).