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…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

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…

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] One of the greatest weaknesses of physics education research is the paucity of research on graduate education. While there are a growing number of investigations of graduate student degree progress and admissions, there are very few…

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…

Collaborative learning with peers can lead to students learning from each other and solving physics problems correctly not only in situations in which one student knows how to solve the problems but also when none of the students can solve the problems alone. We define the rate of construction as the percentage of groups collaborating on problem…

A common task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state. Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin-½ systems. Our…

Pre-service science teachers learn about metacognitive knowledge theoretically in their pedagogy courses; however, teaching practice in science classes reveals the theory-practice gap in their metacognitive knowledge, which has practical importance for prospective teachers. This paper reports on an experiment conducted to investigate the influence…

In quantum mechanics courses, students are often asked to solve bound and scattering state problems. The use of an ordinary differential equation is a standard technique to solve these questions. Here, we investigated students' problem-solving processes for two typical problems of a single particle in one spatial dimension: a bound state problem…

This article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves linear algebra concepts. The particular characteristic of MRC that is the focus of this analysis is students' critiquing and comparing the adequacy of…

With the increasing industrial relevance of new quantum technologies, a well-educated quantum workforce becomes increasingly crucial. The foreseeable lack of workforce raises important questions. What are the expectations regarding the future relevance of second-generation quantum technologies? What are the requirements for the workforce 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'…

Many studies provide insights into students' conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students' initial conceptions, students' transfer of learning of these conceptions to subsequent courses can provide additional…

Analysis of stochastic processes can be used to engender critical thinking. Quantum dots have a reversible, stochastic transition between luminescent and nonluminescent states. The luminescence intermittency is known as blinking and is not evident from ensemble measurements. In order to stimulate critical thinking, students design, perform, and…

Understanding the concepts of quantum mechanics has always been a challenge for undergraduate students. This is especially so because many of the introductory (analytically solvable) systems and problems discussed in textbooks are seemingly abstract. Using approximate experimental demonstrations of such systems and problems have been shown to be…