扩展波包和量子到经典的转变

IF 0.6 4区 教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES
John S Briggs
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引用次数: 0

摘要

大多数教科书对从量子力学向经典力学过渡的标准描述是证明位置和动量的量子期望值服从牛顿形式的方程。这就是艾伦费斯特定理。它与波包保持局部性的要求相结合,描述了根据经典力学运动的单个粒子。因此,波包的自然扩散被视为一种量子效应。与这一观点相反,本文认为,不同动量成分分离的扩散是量子向经典过渡的标志。渐近空间波函数与初始动量空间波函数成正比,这正好反映了光学中著名的远场衍射模式。轨迹被定义为扩展波前的法线位置,用来说明从量子运动到经典运动的转变。这也是光学中从波到光束的转变。建议将这种量子到经典转变的分析纳入量子力学入门课程的常规内容。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Expanding wave packets and the quantum to classical transition
The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.
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来源期刊
European Journal of Physics
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.
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