Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how "eigen" develops over…

Quantum mechanics is notoriously challenging, and research has found that students struggle with many common difficulties when learning it. It is also proving to be a critical piece of many exciting fields that are all but assured to see great development and expansion in the coming years; the Second Quantum Revolution is upon us. Quantum…

Quantum science is in the news daily and engages students' interest and curiosity. A fundamental quantum science concept that underpins medical imaging, quantum computing and many future technologies is quantum spin. Quantum spin can explain many physical phenomena that are in the lower secondary school curriculum, such as magnetism and light,…

We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research but is also important for emerging technologies. However, many students regard quantum mechanics as a particularly challenging subject, in part because it is considered very mathematical and abstract. One potential way…

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.…

Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive theories is steadily increasing, thus opening new areas of interest to discipline-based education research,…

Quantum dots are colloidal semiconductor nanocrystals that display size-dependent electronic and optical properties. These materials are a visual demonstration of a quantum-mechanical effect. Here we present a laboratory exercise for undergraduate/Bachelor students as an introduction to colloidal nanocrystals and quantum dots. The students…

When thinking about measurement uncertainty in a laboratory experiment that features quantum mechanical effects, it is important to consider both the physical principles of underlying quantum theory (e.g., the uncertainty due to quantum mechanical superposition states) as well as the limitations of the measurement (e.g., the spread in outcomes due…

We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were…

Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on…

As part of ongoing research on student thinking about quantum mechanical concepts and formalism, we explored how students defined and made sense of expectation values. Previous research has focused on student difficulties when defining the expectation value for a generic operator and found that students conflate other quantum mechanical ideas with…

The study investigates secondary students' understanding of "orbital" and "electron cloud" concepts in different quantum contexts (for values of the ?principal quantum number n = 1 and n = 2) on the basis of their verbal and pictorial representations, evaluating also their consistency. Participants, which were 192 12th-grade…

Quantum mechanics has proven to be a challenging subject for instructors to teach and conceptually difficult for students to understand. A major source of the difficulty is the lack of everyday experience that quantum mechanics can be related to and the change in thinking required in transitioning from deterministic classical mechanics to a…

As quantum information science and technology (QIST) is becoming more prevalent and occurring not only in research labs but also in industry, many educators are considering how best to incorporate learning about quantum mechanics into various levels of education. Although much of the focus has been on quantum concepts in nonlab courses, current…