This qualitative study investigates students’ knowledge of wave function and operator concepts.The data of the study were collected by semi-structured interviews with 34 pre-service physics teachers and analyzed by using the content analysis method. As a result of qualitative analysis, different categories were determined towards the students’ comprehension of wave function and operator concepts. These results showed that (1) students did not have enough knowledge to define the concepts of wave function and operator properly, (2) they were influenced by the perspective of classical physics in making explanations related to the concepts of quantum mechanics, and (3) a great number of students who participated in the study made explanations by using examples frequently used in quantum mechanics. It is hoped that the results of this study will help the educators to recognize the students’ comprehensions in both modern physics and quantum mechanics courses.
This qualitative study investigates students’ knowledge of wave function and operator concepts.The data of the study were collected by semi-structured interviews with 34 pre-service physics teachers and analyzed by using the content analysis method. As a result of qualitative analysis, different categories were determined towards the students’ comprehension of wave function and operator concepts. These results showed that (1) students did not have enough knowledge to define the concepts of wave function and operator properly, (2) they were influenced by the perspective of classical physics in making explanations related to the concepts of quantum mechanics, and (3) a great number of students who participated in the study made explanations by using examples frequently used in quantum mechanics. It is hoped that the results of this study will help the educators to recognize the students’ comprehensions in both modern physics and quantum mechanics courses.
This qualitative study investigates students’ comprehension of wave function and operator concepts. The data of the study were collected by semi-structured interviews with 34 pre-service physics teachers and analyzed by using the content analysis method. As a result of qualitative analysis, different categories were determined towards the students’ comprehension of wave function and operator concepts. These results showed that (1) students did not have enough knowledge to define the concepts of wave function and operator properly, (2) they were influenced by the perspective of classical physics in making explanations related to the concepts of quantum mechanics, and (3) a great number of students who participated in the study made explanations by using examples frequently used in quantum mechanics. It is hoped that the results of this study will help the educators to recognize the students’ comprehensions in both modern physics and quantum mechanics courses.
Key words: Comprehension, modern physics, operator, physics education, quantum mechanics, wave function.
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.
In this study, we investigated students’ mental models of wave–particle duality. We interviewed six engineering and premedical students enrolled in a calculus-based physics course. We conducted a qualitative examination of student interviews and found that students displayed four different mental models: quantum model (QM), semi-quantum model (SQM), wave model (WM), and in-between model (IM). We also found that 2/3 of the students had difficulty discriminating between classical and quantum ideas and held mental models that were inconsistent and context-specific. This work provides a much-needed detailed exploration of students’ conceptions of quantum theory, which will help instructors understand conceptual barriers frequently encountered by introductory students.
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora's Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora's Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.
Through many years of teaching Quantum Mechanics in Algerian universities, we have noticed that students face great obstacles in understanding the meaning of the basic concepts of this theory, such as the Wave Function, the Uncertainly Principle, the Superposition Principle and the Complementarity Principle. We believe that these obstacles rise due to the influence of basic concepts in Classical Mechanics which students studied for many years before studying Quantum Mechanics. For example, in Classical Mechanics, the concept of wave and the concept of corpuscle refer to different things, while in Quantum Mechanics both concepts refer to the same thing, namely a "quantum particle". In order to study the problem, a questionnaire sheet was presented to concerned students third-year (undergraduate physics students) before they studied the subject and after studying it. We note that these third-year students had had, as an introduction, a deep discussion of the meaning of quantum mechanical concepts for about one hour and a half a week during one month. To compare the results and show the importance of the epistemological and educational aspects, we presented again the same questionnaire to fifth-year physics students (B.Sc degree). We mention that the latter learned Quantum Mechanics without an epistemological introduction of the basic quantum mechanical concepts. Before giving our epistemological and didactical analysis of the results, we give a brief review of a previous didactical study related to the subject made by other authors. We conclude by giving some suggestions which we think are necessary in teaching Quantum Mechanics.