Integrating Dirac approach to quantum mechanics into physics teacher education

Tóth, Kristóf

doi:10.1063/5.0150429

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…(3) It may be advisable for the mixed and functional thinking students to continue the course with the introduction of a simplified quantum formalism (Michelini et al, 2002(Michelini et al, , 2022bTóth, 2023Tóth, , 2024.…”

Section: Discussionmentioning

confidence: 99%

“…Two properties are incompatible if the possession of one makes the possession of the other uncertain. This is, where the uncertainty principle appears (for deeper explanation, see Tóth, 2023Tóth, , 2024Tóth & Tél, 2023): incompatible properties exist in QM. Two incompatible properties cannot certainly be associated with a system simultaneously, one of them will always remain uncertain; but the uncertain one can also be measured with a given probability.…”

Section: Lesson 2: Uncertainty Principlementioning

confidence: 99%

“…One of the first developments of Dirac approach in secondary school material was carried out by researchers from Udine (Ghirardi et al, 1996;Michelini et al, 2000). They introduced the elements of quantum concepts and simplified mathematics through easy-to-implement student experiments and single photons thought experiments (Cobal et al, 2002a(Cobal et al, , 2002bMichelini, 2008;Michelini & Stefanel, 2006, 2014, 2023. In addition, many educational pathways making use of light polarization have been developed to introduce university students (French & Taylor, 1978;Singh, 2008;Tóth, 2023Tóth, , 2024 and secondary school learners to QM (Migdał et al, 2022;Müller & Wiesner, 2002;Schlummer et al, 2022) and to quantum computing (Berbhardt, 2019;Bondani et al, 2022;Migdał et al, 2022;Walsh et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we present a new teaching-learning sequence, which comprises five lessons (45 minutes each) that requires almost no mathematics and focuses on the basic concepts for lower secondary school students. The presented learning path relies on the previous materials of Udine (Cobal et al, 2002a(Cobal et al, , 2022bGhirardi et al, 1996; 2 / 16 Michelini, 2008;, 2023Michelini et al, 2000Michelini et al, , 2011.…”

Section: Introductionmentioning

confidence: 99%

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From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking

Tóth,

Michelini,

Bitzenbauer

2024

EURASIA J Math Sci Tech Ed

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In this paper, we present a new minimal mathematical conceptual approach to quantum mechanics using light polarization for lower secondary school students with the aim of bringing students closer to the so-called quantum mechanical way of thinking. We investigated how students think about some of the basic concepts and fundamental laws and we found that certain concepts are quite well-understandable in younger grades too. We studied the introduction of the so-called state circle, which can faithfully represent quantum mechanical formalism without involving students in abstract algebraic calculations. We then categorized and analyzed students’ thoughts on the superposition principle and the lack of trajectory, finding that the concept of measurement and the lack of trajectory were problematic. We explored that younger students tend to hold gestalt-like mental models of quantum concepts, while at the same time being able to use visualizations correctly for reasoning in the quantum realm. Overall, this paper provides evidence in favor of introducing basic features of quantum mechanics as early as in lower secondary school.

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Section: Discussionmentioning

confidence: 99%

Section: Lesson 2: Uncertainty Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking

Tóth,

Michelini,

Bitzenbauer

2024

EURASIA J Math Sci Tech Ed

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Quantum uncertainty: what to teach?

Tóth

Tél

2023

Phys. Educ.

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We present a new secondary school teaching method of quantum uncertainties of two-state systems. Intending to be a material teachable in schools, only two-state systems described by real numbers can be considered. An elementary argumentation based on school statistics leads to the identification of the uncertainty of a physical quantity in such systems with the standard deviation of two random variables. We provide a qualitative picture on the state-dependence of the uncertainty, leading to a pictorial representation in the form of four petals of a flower. When considering the product of uncertainty of two essentially different physical quantities we conclude that the general feature: “if the measurement of one of the quantities is certain, the other remains uncertain”, cannot be faithfully expressed by means of an inequality, the product has no lower bound different from zero. The application of techniques used by school materials for teaching quantum physics leads to an exact formula for the state-dependence of the uncertainty valid in any two-state system described by real numbers, in full harmony with the qualitative picture. We compare the two-state case with the celebrated Heisenberg position-momentum uncertainty relation and show that these are both specific facets, but only the Heisenberg relation can be expressed by an inequality. The latter hardly provides any hint on the uncertainties of physical quantities in two-state systems. We conclude that the two-state approach is worth teaching in schools also in relation to the uncertainty relation, even if the Heisenberg relation is not part of the curriculum.

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Dirac’s Approach to Quantum Mechanics in Physics Teacher Education: From Linear to Circular Polarisation

Tóth

2024

J. Phys.: Conf. Ser.

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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.

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Integrating Dirac approach to quantum mechanics into physics teacher education

Cited by 5 publications

References 11 publications

From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking

From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking

Quantum uncertainty: what to teach?

Dirac’s Approach to Quantum Mechanics in Physics Teacher Education: From Linear to Circular Polarisation

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