Integrating Dirac approach to quantum mechanics into physics teacher education

Kim Krijtenburg-Lewerissa, Wouter van Joolingen, Hendrik Jan Pol +1 more

Kristóf Tóth

Abstract The teaching/learning of quantum mechanics via two-state systems is continuously spreading in secondary schools due to its promising results in physics education research. One possibility is the use of polarisation states of photons. This paper reports on a polarisation-based introduction to quantum mechanics in physics teacher education. A widely used school material prepares teacher trainees for their future work and also improves their conceptual knowledge. This part includes statistical calculations using only secondary school mathematics and a new formulation of the uncertainty relation, using only real numbers. The second step is to prepare the formalism of quantum mechanics using real two-dimensional vectors and matrices. Considering that students may not learn complex linear algebra, we offer a new way to introduce the complete formalism of two-state systems via circular polarisation providing a step-by-step exploration of complex quantum states. This points out the advantage of using complex linear algebra via a physical example, providing the opportunity to reach the elements of advanced quantum physics and quantum computing while deepening the physics background of the secondary school material.

Paola Verrucchi

Kristóf Tóth

Abstract In the 2019/20 school year I directed a teaching unit on quantum mechanics based on light polarization which enriched me with several experiences. Sometimes I faced problems because the obligatory Hungarian curriculum based on the wave nature of particles does not fit perfectly with the polarization approach of quantum physics. Nevertheless, I presented the polarization approach to my physics teacher colleagues too. Then I recognized some of the difficulties of Hungarian physics teachers in relation to this approach because they used to apply the wave approach. Thus, teacher training programmes should include the foundations of different approaches on equal footing, and in my opinion, teacher education should also respond to secondary school opportunities. In this article, I summarize the problems that may arise in applying the polarization approach in countries where wave formalism has a great tradition, like in Hungary. I also show why I personally prefer a 2-state approach in secondary school instead of the traditional wave formalism, and present what I have learned as a teacher. I highlight some of the requirements that arise when we intend to use polarization approach in physics teacher training programmes, and I make suggestions for teacher education too.

Gesche Pospiech

Marco Giliberti