固体物理中使用Lambert W函数的新解析结果

IF 0.6 4区教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES

European Journal of Physics Pub Date : 2023-10-05 DOI:10.1088/1361-6404/ad009d

Ahmed Houari

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引用次数: 0

摘要

在物理学中，为了数学的完备性，解析解总是被偏爱的。为此，我利用Lambert W函数，导出了离子晶体中平衡离子间距离、晶体中空位形成能量、清洁极限超导体的零温度能隙和2D-XY模型中相变的临界Kosterlitz-Thouless温度的封闭解析表达式。除了它们的理论意义之外，目前的一些结果还提出了有关物理量的其他实验确定方法。此外，我同样导出了一个基于Lambert W函数的显式解析公式，用于确定玻尔兹曼常数。本文提出该公式，作为测量该常数的实验方法的理论基础。这种方法适合物理本科学生。

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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New analytical results in solid state physics using the Lambert W function

Abstract Analytical solutions in physics are always preferred for the sake of mathematical completeness. For this, using the Lambert W function, I derive closed-form analytical expressions for the equilibrium interionic distance in an ionic crystal, the formation energy of a vacancy in a crystal, the zero-temperature energy gap of a clean-limit superconductor and the critical Kosterlitz-Thouless temperature for the phase transition in 2D-XY model. Besides their theoretical interest, some of the present results suggest alternative experimental determinations of the relevant physical quantities. In addition, I similarly derive an explicit analytical formula based on the Lambert W function for a determination of the Boltzmann constant. This formula is proposed here as a theoretical basis for an experimental method to measure this constant. This method is suitable for undergraduate physics students.

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来源期刊

European Journal of Physics 物理-物理：综合

CiteScore

1.70

自引率

28.60%

发文量

128

审稿时长

3-8 weeks

期刊介绍： European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education. Authors submitting articles must indicate the usefulness of their material to physics education and make clear the level of readership (undergraduate or graduate) for which the article is intended. Submissions that omit this information or which, in the publisher''s opinion, do not contribute to the above mission will not be considered for publication. To this end, we welcome articles that provide original insights and aim to enhance learning in one or more areas of physics. They should normally include at least one of the following: Explanations of how contemporary research can inform the understanding of physics at university level: for example, a survey of a research field at a level accessible to students, explaining how it illustrates some general principles. Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks. Descriptions of novel laboratory exercises illustrating new techniques of general interest. Those based on relatively inexpensive equipment are especially welcome. Articles of a scholarly or reflective nature that are aimed to be of interest to, and at a level appropriate for, physics students or recent graduates. Descriptions of successful and original student projects, experimental, theoretical or computational. Discussions of the history, philosophy and epistemology of physics, at a level accessible to physics students and teachers. Reports of new developments in physics curricula and the techniques for teaching physics. Physics Education Research reports: articles that provide original experimental and/or theoretical research contributions that directly relate to the teaching and learning of university-level physics.