In this study, we offer several grades of abstractness and representation of a two-state system as part of quantum physics (QP) teaching. The teaching was implemented as part of a study dealing with quantum physics teaching in high school, but some of the conclusions are also relevant to teaching quantum physics at a university or college level.
A quantum physics curriculum has been developed. The curriculum is for high school students. The program was based on the Discipline-Culture approach (Tseitlin & Galili, 2005; Weissman et al, 2019). In this approach, each physical theory is presented in a triadic structure: nucleus - basic principles, body - applications, and periphery - alternative understandings (misconceptions, and understandings based on other theories). In this talk we will mainly address the nucleus and body of QP.
An application that can expose students to the nucleus principles of QP is a two-state system, that is, a system described by the two-dimensional Hilbert space. In such a system, the principles of superposition, measurement, probability, and uncertainty could be presented.
This system can be represented in a number of ways with different levels of abstraction. These levels are: experimental (e.g. Stern-Gerlach Apparatus), model experiment (e.g. polarizers), verbal description an analogy (introducing the concept of “spin” by oral and text explanations) symbolic (Dirac notation with symbols), algebraic (Dirac notation that relate to axes that not necessarily perpendicular to each other). (Pospiech et al, 2019)
An examination of students' conceptual understanding, as well as their computational ability, showed evidence of a significant understanding of the basic principles and their application. The multiplicity of representations helped to understand and create a connection between the computational ability and the conceptual.
References
Pospiech et al (2019). Symposium at GIREP 2019 conference, 1-5 July, Budapest, Hungary.
Tseitlin, M. & Galili, I. (2005). Teaching physics in looking for its self: from physics as a discipline to physics as a discipline -culture. Science & Education, 14 (3-5), 235-261.
Weissman, E. Y., Merzel, A., Katz, N., & Galili, I. (2019). Teaching quantum mechanics in high-school─ Discipline-Culture approach. Journal of Physics: Conference Series, 1287 (1), p. 2003. IOP Publishing.‏