One expected outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some they have not previously encountered. To investigate student understanding of the relationships…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

The Poisson distribution describes the probability of a certain number of events occurring in an interval of time when the occurrence of the individual events is independent of one another and the events occur with a fixed mean rate. Probably the best-known example of the Poisson distribution in the physics curriculum is the temporal distribution…

Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam…

Research on teaching and learning quantum physics (QP) frequently explores students' conceptual difficulties to identify common patterns in their reasoning. The abstractness of QP is often found to be at the origin of students' conceptual difficulties. Due to this abstract nature students resort to common sense reasoning or classical thinking when…

The Born rule, which describes the formalism for determining probabilities, is one of the most fundamental postulates in quantum mechanics. This paper presents results from an investigation into how students apply the Born rule to determine probabilities for energy and position measurements. The investigation includes two stages with independent…

Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a…

Quantum mechanics is a notoriously counterintuitive subject within physics and has been the subject of a number of studies at the undergraduate level, and a few pioneering studies at the graduate level. The sketching of wave functions in a confining well is in one sense one of the most basic activities in quantum mechanics. But in another sense,…

The Maxwell distribution of speeds, f(v), is the starting point for the calculation of the transport coefficients in kinetic-molecular theory. Most physical chemistry textbooks follow a path to derive f(v) similar to that used by Maxwell, which makes it difficult for students to understand its relationship with the equilibrium state of the system,…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

Explanations of phenomena in chemistry are grounded in discussions of particulate-level behavior, but there are limitations to focusing on single particles, or as an extension, viewing a group of particles as displaying uniform behavior. More sophisticated models of physical processes evoke considerations related to the dynamic nature of bulk…

This article describes the development of the Quantization and Probability Representations Inventory (QuPRI) as a measure of student understanding of the electron structure of the atom. The QuPRI was created using a mixed-method sequential design such that the items and distractors were generated on the basis of the analysis of semi-structured…

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community's social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic,…

"Tutorials in Physics: Quantum Mechanic" is a set of curricular materials for supplementing upperdivision quantum mechanics instruction, developed by the physics education group at the University of Washington. We describe the development of a sequence of three tutorials that focused on quantum measurements and time dependence. This…