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…

The Uncertainty Principle is usually discussed twice in a Quantum Chemistry course. The first discussion is a "pre-wave function" explanation that occurs before students know about wave functions, but "do" know the de Broglie hypothesis. The second description of the Uncertainty Principle is "post-wave function",…

In this article we offer a conceptual and practical contribution to the field of STEM education by investigating the concepts educators may include in Quantum Technologies (QT) outreach activities. We embed our approach in the discipline-culture (DC) framework, in which we consider the cultural nuances of QT as an important factor which must not…

Reasoning with mathematics plays an important role in university students' learning throughout their courses in the scientific disciplines, such as physics. In addition to understanding mathematical concepts and procedures, physics students often must mathematize physical constructs in terms of their associated mathematical structures and…

As part of an effort to examine students' mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue…

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…

In this paper, we present a computational chemistry project that demonstrates the quantum dynamics of a free particle, using both classical and quantum computing algorithms. This project can be used in a computational quantum chemistry course in which the instructor introduces quantum computing. Students write their own programs to simulate the…

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 course-based undergraduate research experiences (CURE) approach is increasingly being used in undergraduate experimental courses. Here, we describe the implementation of CURE in an upper-level inorganic chemistry course, in which students were assigned different current themes to study. This paper focuses on the theme of quantum dots,…

Periodicity in electronic molar entropy values has been shown on the basis of the electronic structures of the elements. Also, with the approximations discussed herein, one can estimate the electronic molar entropy without atomic spectroscopy results. All of this can be accomplished by showing the connection between the vector model of the atom…

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,…

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study…

Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in experiments in undergraduate instructional labs. Here, we present results from an interview study about what it…

We outline the physics involved in the use of scanning electron microscopy (SEM) and modernise the usual textbook treatment by explaining how one can now obtain high-quality images with non-conductive specimens. As a concrete example of an application in biology, we provide several magnification series of a flea obtained using SEM.

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.…