Probing student reasoning in relating relative phase and quantum phenomena

Abstract

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore-and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1=2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.

Towards a better understanding of conceptual difficulties in introductory quantum physics courses

“…The 'conceptual change' perspective allowed us to highlight that students' conceptual difficulties in QP originate in a deeply rooted conceptual framework that is stable over time and resistant to change and QP education should aim to restructure students' conceptual frameworks (e.g., Ayene et al, 2019;Kalkanis et al, 2003;Oh, 2011). The 'mental models' perspective can illustrate that students' prior ideas are not elaborated or stable, and students' reasoning can depend on the physical context as well as on the framing of the problem (Didiş et al, 2014;Hubber, 2006;Wan et al, 2019). Conceptual difficulties surface as students struggle to make meaning, and their reasoning is based on the inappropriate activation of contextdependent cognitive or meta-cognitive resources.…”

“…Students' meaning-making process is at the centre of students' conceptual difficulties when learning QP (e.g., Modir et al, 2019;Wan et al, 2019). Students learning QP construct knowledge for themselves where their prior ideas serve as both a foundation and building material for constructing new (i.e.…”

“…Students learning QP construct knowledge for themselves where their prior ideas serve as both a foundation and building material for constructing new (i.e. QP) knowledge (e.g., Malgieri et al, 2017;Modir et al, 2019;Taber, 2005;Wan et al, 2019). Conceptual difficulties occur when students try to interpret new knowledge in their existing conceptual framework (e.g., Duit & Treagust, 2003;Vosniadou, 1994;Vosniadou et al, 2008).…”

“…In this literature review, we intend to combine findings from different theoretical perspectives and different strands of research to arrive at a synthesis that describes both the origin of students' conceptual difficulties in QP and reasons why these difficulties prolong for an extensive period while students learn QP. Students' meaning-making process is at the origin of students' conceptual difficulties, as students are confronted with new situations they face while reasoning (e.g., Modir et al, 2019;Taber, 2005;Wan et al, 2019). Students' conceptual difficulties often persist over an extensive period of time, as students are unaware that their underlying assumptions derived from a mainly classical conceptual framework are invalid (e.g., Oh, 2011).…”

Investigating students’ strategies for interpreting quantum states in an upper-division quantum computing course

“…In 2006, Singh [5] discussed specific student difficulties in quantum mechanics of particular relevance to quantum computing applications. Though explicit references to quantum information science are otherwise sparse in the literature, a number of subsequent publications have elucidated additional student difficulties relevant to QIS education [6][7][8][9][10]. Notably for our context, Passante et al [6] found that more than half of surveyed undergraduate and beginning graduate students failed to distinguish between an ensemble of particles in a superposition state (in this case,…”