The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.
Abstract The Heisenberg uncertainty principle (HUP) plays an important role in quantum mechanics. It is necessary to demonstrate this principle experimentally for undergraduates to understand HUP clearly. In this paper, we originally employ the quantum quadrature operators to demonstrate HUP in undergraduate laboratories. Starting from the quantization of electromagnetic field, we briefly review the definition of quadrature operators and demonstrate HUP via the variances of quadrature operators. And the scheme of HUP demonstration with homodyne detection is introduced. More importantly, we develop a tabletop experimental apparatus for the demonstration of HUP in undergraduate laboratories. Our proposal focuses on the basic quantum mechanics concepts, experimental principles, and instruction as well as experimental techniques. It provides a way to help undergraduates, especially the ones who will go on graduate study in quantum technology in the future, make connections between abstract quantum mechanics concepts and concrete experiments, which makes the concepts better understood.
With the coming of quantum information and associated technologies, there is increasing need to prepare students on the fundamentals of quantum physics. Fundamental physical principles can be hidden by the mathematical formalism of quantum mechanics. Thus it is necessary to expose students to experiments that illustrate fundamentals. Quantum optics experiments based on the generation of twin photons via spontaneous parametric down-conversion have many advantages, such as being simple, reliable, and of reasonable cost. These types of experiments are ideal for the advanced laboratory in the physics curriculum. At Colgate University we offer them as a laboratory package that is associated with our upper-level undergraduate course on quantum mechanics. In this article we present our latest approaches. Among them is a new layout for the experiments to provide a more intuitive physical picture.
Abstract This paper presents a new lab work concept promoting a series of quantum optics experiments: experimental milestones on the quantum behaviour of light designed for undergraduate lab work. The experiments may be carried out with considerably less effort while addressing the fundamentals of quantum theory: quantum states and their superposition, detected via the propagation phase of probability amplitudes; quantum nonlocality, detected via the change of the state due to localized detection; quantum entanglement , detected via the violation of Bell ’s inequality (CHSH criterion). The experimental setup is designed to meet the requirements of barrier-free multilevel use in undergraduate physics lab courses: students’ labs for secondary school students, undergraduate university labs for physics students (science and science education) and lab work assisted courses for the training of in-service physics teachers. This article is aimed to describe the basics of the setup and to show how the experiments may be implemented into lab courses to match different educational course levels. The experimental series could prove to be promising in terms of fruitful discussion of quantum theory fundamentals without semiclassical pitfalls.
Abstract Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.
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.
Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. \nWith regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn.