吉布斯现象与弗里德尔振荡：相似性、差异及其比较的教育潜力
Gibbs Phenomenon and Friedel Oscilations: Similarities, Differences, and the Educational Potential of their Comparison
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中文总结 AI 辅助
探究不连续信号的吉布斯现象与固体电子密度的弗里德尔振荡的异同，从工程师视角详细探索，以一维电子气密度为例表明二者有别，但其相似性可培养直觉并促进电气工程师与凝聚态物理学家交流。
中文摘要 AI 辅助
我们探究了不连续信号的部分傅里叶表示中的吉布斯现象与固体中靠近异常处电子密度的弗里德尔振荡之间的异同。受这两种现象明显相似性的启发，从向工程师介绍固态物理概念的角度对两者进行了详细探究。聚焦于由方势阱限制的一维电子气的密度，表明尽管有相似性，但弗里德尔振荡不能归因于部分傅里叶级数无法描述不连续性。不过，这两种现象确实存在相似性，可用于培养直觉。采用教育方式，希望在电气工程师和凝聚态物理学家之间建立共同语言，以进一步激发两个群体在相邻但不同学科中寻求直觉和深入理解。
英文摘要
We explore the similarities and differences between the Gibbs phenomenon in partial Fourier representations of discontinuous signals and Friedel oscillations in the electron density of a solid near an anomaly. Inspired by the apparent similarities of the two phenomena, we perform a detailed exploration of both from the viewpoint of an engineer being introduced to a concept from solid-state physics. Focusing on the density of an one-dimensional electronic gas confined by a square potential, we show that, despite the similarities, Friedel oscillations cannot be attributed to the inability of a partial Fourier series to describe a discontinuity. Nevertheless, the two phenomena do exhibit similarities, which can be exploited to develop intuition. By adopting an educational style, we hope to establish some common language between electrical engineers and condensed-matter physicists, hoping that this can further inspire the two communities to seek intuition and further comprehension within neighbouring but different disciplines.
