Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics
Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics
复制标题
研究并提高学生对量子力学中测量物理可观测量的概率分布的理解
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
C. Singh
中科院分区：
文献类型：
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作者：
E. Marshman;C. Singh
牢固掌握测量物理可观测量的概率分布是将量子形式主义与测量联系起来的核心。然而，学生经常对可观察的测量结果的概率分布感到困惑，并且很难以不同的表示形式表达这个概念。在这里，我们首先描述高年级本科生和博士生在测量量子力学中物理可观测量的概率分布方面遇到的困难。然后，我们讨论如何将学生在书面调查和个人访谈中发现的困难用作开发量子交互式学习教程（QuILT）的指南，以帮助学生更好地掌握物理可观察量的测量结果的概率分布。 QuILT 致力于帮助学生熟练地用狄拉克表示法和位置表示法表达物理可观测量测量的概率分布，并能够从狄拉克表示法转换为位置表示法，反之亦然。我们描述了 QuILT 的开发和评估以及课堂评估中有关 QuILT 有效性的发现。
A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.