Research into student understanding of quantum mechanics has primarily focused on the identification of student difficulties a nd t he d evelopment o f c urriculum t hat c an h elp i mprove s tudent l earning.M ost o f this work has been performed in courses using a position-first i nstructional p aradigm.R ecently, t here h as been increase in the number of instructors choosing to present material in an alternate order: spins-first.In this work, we makes steps towards answering the question of whether or not the instructional paradigm has an impact on student thinking about energy measurement.We use a resources lens to analyze the different tools and methods students are using to solve questions.
Research into student understanding of quantum mechanics has primarily focused on the identification of student difficulties a nd t he d evelopment o f c urriculum t hat c an h elp i mprove s tudent l earning.M ost o f this work has been performed in courses using a position-first i nstructional p aradigm.R ecently, t here h as been increase in the number of instructors choosing to present material in an alternate order: spins-first.In this work, we makes steps towards answering the question of whether or not the instructional paradigm has an impact on student thinking about energy measurement.We use a resources lens to analyze the different tools and methods students are using to solve questions.
The Paradigms team at Oregon State University has developed a quantum mechanics curriculum aimed at middle division students that begins with a strong emphasis on using operators, matrices and Dirac notation to describe quantum systems. The curriculum begins with spin systems, and this content ordering relies on students being able to understand quantum mechanical operators, eigenstates and quantum measurement without prior instruction on wave functions. We have analyzed classroom and an interview video to identify resources students use when considering these quantum ideas. Identification of such resources will inform introductory curricula that are prerequisite to the quantum Paradigms and inform the development of Paradigms materials that will guide students to use these resources productively.
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.
As part of ongoing research to better understand how students relate Quantum Mechanics concepts to formalisms, we are studying student understanding of expectation values as well as the variety of mathematical representations they use for formalizing them in two different teaching paradigms.Analyzing students' written responses to a series of open-ended research questions has given us some insight into students' common interpretations of this concept, as well as the frequency of the various mathematical formalisms they use to represent expectation values.The results show some common patterns between students in Spin First (SF) and Position First (PF) curricular, as well as some differences.
This paper is part of the Focused Collection on Upper Division Physics Courses.]Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction.We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function and Hamiltonian, to determine the probabilities of each energy measurement and how they depend on time, and to recognize how a measurement of energy affects the state.By analyzing student responses to open-ended questions, we identify five broad, interrelated sets of conceptual and reasoning difficulties related to energy measurements.Data are drawn from sophomore-, junior-, and graduate-level quantum mechanics courses.Particular attention is paid to incorrect ideas that persist across all levels.
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 task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state.Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin-½ systems.Our investigation is based on conceptual and computational written questions as well as student reasoning interviews.We identify student ideas about whether and how changing basis affects the state, examine how students perceive notation as indicative of choice of basis, explore students' interpretations of the structure and meaning of a basis expansion, and identify the range of methods students employ when changing basis.For instance, we find a recurring idea that changing basis alters the physical system, and observe that some students chose to relabel the ket representing a quantum state vector after changing basis.Together, these results paint a broad, qualitative picture of a variety of ways that students grapple with basis and change of basis, with potential implications for instruction.