Research-validated clicker questions comprise an easy-to-implement instructional tool that can scaffold student learning while formatively assessing students’ knowledge. We present findings from the development, validation and implementation, in consecutive years, of a Clicker Question Sequence (CQS) on measurement uncertainty as it applies to two-state quantum systems. This study was conducted in an advanced undergraduate quantum mechanics course, in both an online and in-person learning environment. Student learning was first assessed after receiving traditional lecture-based instruction on relevant concepts, and their performance on it was compared with that on a similar assessment given after engaging with the CQS. We analyze and discuss similar and differing trends observed in the two modes of instruction. 

As part of a broad project to improve the teaching and learning of undergraduate quantum mechanics, we have developed a suite of instructional materials that are easy to implement into a variety of instructional contexts.  These materials are freely available online and are modular, adaptable, and include clicker questions, sample lecture notes, tutorials (both in person and online), preflights, homework and exam questions, as well as an end-of-course conceptual survey.  Our newly designed online tutorials allow for many of the benefits of tutorials without taking up valuable class time.  They provide dynamic feedback to students and can be assigned for out-of-class use either as individuals or for groups.  Stop by our poster to see examples of all these materials and chat with us about what might work best for your instructional setting.

Physics learners are confronted with many new, frequently abstract, concepts as well as new technical language that describes them. Making sense of abstract ideas, like physical states or fields, is influenced by the conceptual metaphors instructors use when speaking about them. Students also construct understanding about the ontology of physical concepts through clues in the functional grammar used. Sense-making through interpreting language is particularly relevant to connecting the mathematical abstraction of theory to the concrete physical phenomena. Quantum mechanics presents a particular challenge to learners; not only is the theory an abstraction of the physical phenomena, but the physical phenomena themselves are outside of human concrete experience. 

Previous work has shown that students have difficulty with concepts such as quantum states, observables, results of measurements, and their mathematical counterparts. Since these concepts are foundational in quantum theory, a conceptual understanding of their uses and ontological distinctions is essential. We present results of an exploratory study to examine the conceptual metaphors and ontological categorization that students and instructors use when speaking about these concepts in the context of a spins-first curriculum. Our goal is to elucidate language-based difficulty with learning quantum mechanics concepts.

Quantum mechanics is a field often considered very mathematical and abstract. To make quantum more concrete, some instructors expose their students to fundamental quantum phenomena in an experimental setting. This can be done in undergraduate instructional labs with a sequence of quantum optics experiments referred to as the single-photon experiments. Here, we present results from an interview study about what it means to both instructors and students to see quantum effects in experiments. Focusing on the single-photon experiments, we find that students believe they are observing quantum effects and achieving related learning goals. Although it is not possible to see the quantum phenomena directly with their eyes, students point out different aspects of the experiments that contribute to them observing quantum effects. There is also variation across student achievement of related learning goals, ranging from many of the students being excited about these experiments and making a connection between the mathematical theory and the experiment to only some of the students seeing a connection between these experiments and quantum technologies. This work can help instructors consider the importance and framing of quantum experiments.

There are two types of momentum associated with waves: the “canonical” momentum that is proportional to the velocity of the material and the “field” or “wave” momentum associated with force and propagation of energy in the form of waves. It logically follows that there are also two corresponding types of angular momentum in continuous media: “intrinsic” or “spin” angular momentum associated with rotations in the medium and “wave” or “orbital” angular momentum associated with wave propagation and torque. Spin density is uniquely defined from a Helmholtz decomposition of momentum density as the field whose curl is equal to twice the incompressible component of momentum density. It is related to the usual “moment of momentum” density through integration by parts. Local torque density and force density are similarly related. Equating torque density with the motion-compensated time derivative of spin density is equivalent to stating that total angular momentum is locally conserved. A wave equation is derived for spin density in an elastic solid, and its relation to the Dirac equation of relativistic quantum mechanics is explained.