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…

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…

Broadly speaking, many physicists value intuition in their work, and many instructors hope their students develop intuition (while possibly being wary of their initial, unrefined intuitions). These considerations are especially relevant in quantum mechanics, a subject many see as counterintuitive because it is removed from classical everyday…

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…

In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in…

In an attempt to address the need for an alternative presentation of the quantum mechanical position and momentum spaces, we provide a presentation that is more constructive and less calculative than those found in literature. Our approach is based on a simple, intuitively understood relation that expresses the physical equivalence of the quantum…

The climate emergency mandates a refocusing of society and education on the relationship between humans and the more-than-human world. Emerging from decades of social constructionism that openly promoted climate science denial, social and educational theorising now engages with new materialist philosophies and the agency of matter. Physicist Karen…

It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors…

Eigenstates of a quantum mechanical system reflect one to one correspondence with energy level. However, in some systems more than one or a group of eigenstates correspond to a single eigenvalue. To introduce more than one eigenstate corresponding to single energy eigenvalue in 1D-harmonic oscillator, we introduce a new perturbation term and find…

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The modern physics course is a crucial gateway for physics majors as it provides an introduction to concepts beyond the scope of the K-12 education. This study collected 167 modern physics syllabi from 127 U.S. research-intensive…

In contrast to the determinist and non-discrete structure of classical physical concepts, the probabilistic and discrete/quantised structure of quantum physics embeds certain difficulties in deeper understanding and teaching activities. In this study, in order to understand and to teach the concept of quantization more effectively, a clear analogy…

We calculate the frequency of matter-wave of electrons orbiting the hydrogen nucleus at the ground state. It is the same as the value of light frequency corresponding to the ground state from the Rydberg's formula. The result will stimulate students' interest to further understand the mechanisms of quantum theory.

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only…

Background: Quantum physics has found its way into upper secondary school physics curricula worldwide. This trend coincides with increased attention for conceptual understanding in physics education in general and quantum physics education in particular. Students' conceptual difficulties of learning quantum physics are regularly reported. Little…

Magnetic resonance is a quantum phenomenon and describes a resonant interaction of spins with electromagnetic fields. Its understanding requires advanced knowledge of quantum mechanics and condensed matter physics and thus often remains elusive to students. However, the great impact of this phenomenon on medicine, science, and technology makes…