Framework for understanding the patterns of student difficulties in quantum mechanics

Abstract

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics. I. INTRODUCTIONA solid grasp of the fundamental principles of quantum physics is essential for many scientists and engineers. However, quantum physics is a technically difficult and abstract subject. The subject matter makes instruction quite challenging, and even capable students constantly struggle to develop expertise and master basic concepts.In order to help students develop expertise in quantum mechanics, one must first ask how experts compare to novices in terms of their knowledge structure and their problem-solving, reasoning, and metacognitive skills. According to Sternberg [1], some of the characteristics of an expert in any field include: 1) having a large and well organized knowledge structure about the domain; 2) spending more time in determining how to represent problems than searching for a problem strategy (i.e., more time spent analyzing the problem before implementing the solution); 3) working forward from the given information in the problem and implementing strategies to find the unknowns; 4) developing representations of problems based on deep, structural similarities between problems; 5) efficient problemsolving; when under time constraints, experts solve problems more quickly than novices, and 6) accurately predicting the difficulty in sol...

Probing student reasoning in relating relative phase and quantum phenomena

“…Previous studies on student understanding of quantum mechanics have tended to center on conceptual understanding [1][2][3][4][11][12][13][14][15][16][17]. Recently, there is a growing effort to research how students make sense of mathematical expressions in quantum mechanics [18,19].…”

Effectiveness of interactive tutorials in promoting “which-path” information reasoning in advanced quantum mechanics

“…These two cohorts of graduate students showed identical performance on the other DSE questions, which did not have analogous situations discussed in the MZI QuILT, suggesting that the improved performance on the DSE polarizer questions is likely due to the MZI QuILT helping students discern the underlying principles required to answer questions about interference by using WPI reasoning. We note however that the number of graduate students the DSE → MZI cohort was small (14), and thus it is possible that the encouraging results can be at least in part accounted for by the small number of students. We also note that due to lack of participation from faculty members teaching the upper level undergraduate quantum mechanics course, we were unable to investigate the DSE → MZI condition for undergraduate students.…”

Developing and evaluating an interactive tutorial on degenerate perturbation theory

“…Quantum mechanics (QM) is a particularly challenging subject for upper-level undergraduate and graduate students in physics [1][2][3][4]. Guided by research studies conducted to identify student difficulties with QM and findings of cognitive research, we have been developing a set of researchbased learning tools including the Quantum Interactive Learning Tutorials (QuILTs) [5][6][7]. Here, we discuss an investigation of student difficulties with degenerate perturbation theory (DPT) and the development and evaluation of a researchbased QuILT that makes use of student difficulties as resources to help them develop a solid grasp of DPT.…”