This report shares analysis regarding students’ meta-representational competence (MRC) that is expressed as they engaged in solving a quantum mechanics problem that involved linear algebra concepts. The particular characteristic of MRC that is the focus of this analysis is students’ critiquing and comparing the adequacy of representations, specifically matrix notation and Dirac notation, and judging their suitability for various tasks (diSessa, 2004). With data of students’ work on an expectation value problem from semi-structured individual interviews, students’ MRC was analyzed and categorized according to value-based preferences, problem-based preferences, and purpose and utility awareness. Detail is provided on two students who serve as paradigmatic examples of students’ power and flexibility in thinking in and using different notation systems. In addition to adapting MRC as a helpful construct for characterizing student understanding at the intersection of undergraduate mathematics and physics, we aim to demonstrate how students’ rich understanding of linear algebra and quantum mechanics includes and is aided by their understanding and flexible use of different notational systems.

中文翻译：

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量子力学中矩阵表示法和狄拉克表示法的学生元表示能力

本报告分享了有关学生的元表征能力（MRC）的分析，该能力是在学生参与解决涉及线性代数概念的量子力学问题时表达的。该分析重点关注的MRC的特殊特征是学生批判和比较表示形式（尤其是矩阵表示法和Dirac表示法）的适当性，并判断其对各种任务的适用性（diSessa，2004年）。利用来自半结构化个人访谈的学生关于期望值问题的工作数据，根据基于价值的偏好，基于问题的偏好以及目标和效用意识对学生的MRC进行了分析和分类。提供了两个学生的详细信息，它们是学生思考和使用不同符号系统的能力和灵活性的典范示例。