{"title":"New analytical results in solid state physics using the Lambert W function","authors":"Ahmed Houari","doi":"10.1088/1361-6404/ad009d","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1361-6404/ad009d","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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