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Challenges in physics education

The Role of Mathematics in Teaching Quantum Physics at High School

Gesche Pospiech, Avraham Merzel, Giacomo Zuccarini, Efi Weissman, Nadav Y. Katz, Igal Galili, Lorenzo Gianni Santi, Marisa Michelini

Published Jan 1, 2021• 20 citations
Publisher
DOI
10.1007/978-3-030-78720-2_4

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Abstract Quantum Key Distribution (QKD) is a cryptography protocol based on the fundamental principles of quantum physics (QP). Teaching this subject does not require extensive knowledge beyond these principles, making it suitable for inclusion in high school (HS) curricula. Despite its relevance, teaching QKD in HS is yet understudied. In this study, we collected responses from 12th-grade students from various schools that adopted and applied the Discipline-Culture vision of the physics curriculum. We assessed their understanding through conceptual and quantitative problems and examined their attitudes regarding the motivation to study this subject. We analyzed the responses using content analysis, identifying the challenges and affordances of teaching QKD. The challenges faced by students have been categorized into three themes: difficulties with QP, difficulties with the QKD protocol, and difficulties with the mathematics involved in this context. Despite these challenges, we found that teaching QKD reinforces students’ conceptual understanding of QP concepts and problem-solving skills. This work enhances educators’ ability to address the challenges of teaching QP and suggests that teaching QKD in HS strengthens students’ motivation to study QP.
The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious quantum physics, while avoiding most of the mathematics. In a Dutch quantum physics project for secondary schools, this model was adopted to play a key role. Much to our surprise, we ran into many more applications than we originally expected. In many instances the model yields order of magnitude estimates, for instance of atomic and nuclear size, or qualitative insights, for instance about energy levels, molecular bonding and electron pressure. Moreover, either directly or with minor modifications, the particle-in-a-box model provides reasonable approximations of a range of phenomena, including the absorption spectra of organic pigments, the mass of the proton and the spectra of quantum dots.
Using the simplest possible quantum system—the qubit—the fundamental concepts of quantum physics can be introduced. This highlights the common features of many different physical systems, and provides a unifying framework when teaching quantum physics at the high school or introductory level. In a previous TPT article and in a separate paper posted online, we introduced catchy visualizations of the qubit based on the Bloch sphere or just the unit circle (see also Refs. 3–8 for other approaches highlighting the importance of the qubit). These visualizations open the way to understand basic ideas of quantum physics even without knowledge of the underlying mathematical formalism. In addition, simple mathematics can be introduced to describe the qubit as an abstract object and basic unit of quantum information. This generalizes the digital bit as a basic unit of classical information. The proposed visualizations can be used even at the high school level, while the mathematical explanations are of importance when teaching quantum physics at the undergraduate university level. This approach provides a unified framework to introduce common features of all quantum systems, such as the stochastic behavior and state change of a superposition state under measurement.