Abstract Teaching introductory quantum mechanics is challenging, especially to students who have limited knowledge of mathematics. The challenges and approaches are evidenced in a wide range of literature. Our goal is to develop an active engagement module for introductory quantum mechanics that would cover the most important concepts: indeterminism, incompatibility, the difference between superposition and statistical mixture and the role of measurement. To accomplish this, we developed a free on-line simulation of a double well—a (pseudo) two-state system—which is able to evidence all of the above concepts. Students perform simulated experiments and build their knowledge from their observations. We present the simulation and the proposed experiments to address the above concepts. We provide a description of the activities and their outcomes as tested with high-school students in different settings. Qualitative analysis of learning outcomes offers evidence that between 60% and 100% of students can reach the following conclusions on their own. (i) The particle is only ever detected in one of the possible states. (ii) The outcome of one experiment cannot be predicted, only its probability can be predicted. (iii) For some pairs of quantities, knowing the value of one quantity exactly precludes the possibility of knowing the value of the other quantity exactly. (iv) A statistical mixture (of eigenstates) is not the same as a superposition state. (v) The measurement affects the time evolution of the system. The most difficult conclusion for students to reach is how exactly the measurement affects the system. The success rates presented here lead us to conclude that the simulated experiments can be very useful when designing an active engagement course on the concepts of quantum mechanics. While the development is done in high-school, we believe the results are also relevant for introductory university level, especially for non-physics students.
Abstract Teaching introductory quantum mechanics is challenging, especially to students who have limited knowledge of mathematics. The challenges and approaches are evidenced in a wide range of literature. Our goal is to develop an active engagement module for introductory quantum mechanics that would cover the most important concepts: indeterminism, incompatibility, the difference between superposition and statistical mixture and the role of measurement. To accomplish this, we developed a free on-line simulation of a double well—a (pseudo) two-state system—which is able to evidence all of the above concepts. Students perform simulated experiments and build their knowledge from their observations. We present the simulation and the proposed experiments to address the above concepts. We provide a description of the activities and their outcomes as tested with high-school students in different settings. Qualitative analysis of learning outcomes offers evidence that between 60% and 100% of students can reach the following conclusions on their own. (i) The particle is only ever detected in one of the possible states. (ii) The outcome of one experiment cannot be predicted, only its probability can be predicted. (iii) For some pairs of quantities, knowing the value of one quantity exactly precludes the possibility of knowing the value of the other quantity exactly. (iv) A statistical mixture (of eigenstates) is not the same as a superposition state. (v) The measurement affects the time evolution of the system. The most difficult conclusion for students to reach is how exactly the measurement affects the system. The success rates presented here lead us to conclude that the simulated experiments can be very useful when designing an active engagement course on the concepts of quantum mechanics. While the development is done in high-school, we believe the results are also relevant for introductory university level, especially for non-physics students.
Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.
Quantum superposition is one of the most challenging concepts in introductory quantum physics. This paper proposes a simple “blended cat” classroom demonstration designed to support the teaching of quantum superposition. The model consists of a double-sided rotating plate displaying two mutually exclusive states. When spun, the images appear visually blended; when stopped, a single state is observed. The demonstration is not intended as a physical representation of a quantum system but as a conceptual tool to initiate discussion about the meaning of superposition and measurement. Through guided questioning, students are encouraged to reflect on what it means for a system to be in a superposed state and how measurement determines observable outcomes. The activity provides an accessible and engaging entry point for introducing quantum superposition in secondary and introductory university physics courses.
Abstract In our teaching approach to quantum mechanics for high schools, we combined a two-state system approach with a matter-wave approach. We developed a simulation of a double well, which has been gradually improved with experience to include all the functionality needed to address the most important concepts of quantum physics. A complementary simulation of a double slit has also been developed to address the introduction of the wave function. A course, based on these simulations has been developed and is currently being tested for the fourth year, still undergoing improvements. Each year a series of formative questions and a pre- and post-test has been administered. We report here how the simulation is used to address the concepts of quantum physics and some preliminary results from the ongoing study of the course.
The Stern–Gerlach experiment can play an important role in teaching the formalism of quantum mechanics. In the context of a finite-dimensional Hilbert space students can learn how to prepare a specific quantum state starting from an arbitrary state, issues related to the time evolution of the wave function and quantum measurement. The Stern–Gerlach experiment can also be used to teach the distinction between the physical space where the experiment is performed and the Hilbert space where the state of the system lies, and how information about the state of the system in the Hilbert space can be exploited to interpret the possible outcomes of the experiment in physical space. Students can learn the advantages of choosing an appropriate basis to make predictions about the outcomes of experiments with different arrangements of Stern–Gerlach devices. The latter can also help students understand that an ensemble of identically prepared systems is not the same as a mixture. We discuss student difficulties with the Stern–Gerlach experiment based on written tests and interviews with advanced undergraduate and graduate students in quantum mechanics courses. We also discuss preliminary data which suggest that the Quantum Interactive Learning Tutorial on the Stern–Gerlach experiment is helpful in improving student understanding of these concepts.
Abstract There is consensus on the goal to introduce Quantum Mechanics in secondary school curricula for its paradigmatic role in the modern physics. In literature a wide spectra of proposals were developed and tested. With the goal to approach the basic ideas of quantum theory by means of active learning, we design a research based educational path in the context of light polarization, offering an open software environment for ideal experiments. Several Intervention Modules with secondary school students were performed, monitoring the learning paths by means of tutorials and pre-post-test for total about 900 students. Here a homogenous sample of 126 students is considered. Qualitative/quantitative data analysis shows coherent line of reasoning developed by students along the quantum concepts, coherent in some case with a hidden variables approach.
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.