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…

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…

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.

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…

The appearance of a unique function in the energy transfer from one system to the other in different physical situations such as electrical, mechanical, optical, and quantum mechanical processes is established in this work. Though the laws governing the energy transformation and its transfer from system to system are well known, here we notice a…

Energy consumption in the world is increasing more and more due to the huge energy request coming from emerging countries such as China, India, etc. To face the challenge of sustainability, a solution may be the use of solar energy, since it is the most abundant renewable energy source on Earth. The electromagnetic energy coming from the Sun can…

Learning the wave-particle dualism of electrons and photons plays a central role in understanding quantum physics. Teaching it requires that the teacher is fluent in using abstract and uncommon terms. We inspect the lexical structures of pre-service teachers' declarative knowledge about the wave-particle dualism of electrons and photons in the…

Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students' solutions to midterm exam questions and utilized think-aloud interviews. We also applied a framework that organizes students'…