重温约束三角势的束缚态

IF 0.6 4区教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES

European Journal of Physics Pub Date : 2024-03-19 DOI:10.1088/1361-6404/ad2ec1

Luiz G M Ramos, Antonio S de Castro

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引用次数: 0

摘要

利用正交函数展开法研究了在不可穿透的墙壁限制的三角势影响下粒子的静止状态。与时间无关的薛定谔方程的特征函数通过使用文献中的一对数列闭式表达式来表示。分析包括具有任意耦合的吸引力和排斥力势。束缚对量子态产生了重大影响，并引入了包括基态在内的双重退化情形。分析扩展到讨论向非约束的过渡。这项研究对于在本科课程中将数学方法应用于物理学和量子力学的教育工作者和学生来说具有特别重要的意义，它为了解势的剖面、边界条件以及由此产生的量子现象之间的复杂关系提供了宝贵的见解。

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Revisiting the bound states of a confined delta potential

The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.

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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.