Guangtian Zhu

Surveying students’ understanding of quantum mechanics in one spatial dimension

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.

Improving students' understanding of quantum mechanics via the Stern-Gerlach experiment

The Stern–Gerlach experiment can play an important role in teaching the formalism of quantum mechanics. In the context of a finite-dimensional Hilbert space students can learn how to prepare a specific quantum state starting from an arbitrary state, issues related to the time evolution of the wave function and quantum measurement. The Stern–Gerlach experiment can also be used to teach the distinction between the physical space where the experiment is performed and the Hilbert space where the state of the system lies, and how information about the state of the system in the Hilbert space can be exploited to interpret the possible outcomes of the experiment in physical space. Students can learn the advantages of choosing an appropriate basis to make predictions about the outcomes of experiments with different arrangements of Stern–Gerlach devices. The latter can also help students understand that an ensemble of identically prepared systems is not the same as a mixture. We discuss student difficulties with t...

Cognitive Issues in Learning Advanced Physics: An Example from Quantum Mechanics

We are investigating cognitive issues in learning quantum mechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and conceptual aspects of quantum mechanics and for ensuring that the learning tools help students build a robust knowledge structure. We discuss the cognitive aspects of quantum mechanics that are similar or different from those of introductory physics and their implications for developing strategies to help students develop a good grasp of quantum mechanics.

Improving students' understanding of quantum mechanics by using peer instruction tools

Quantum mechanics is a challenging subject, even for advanced undergraduate and graduate students. Here, we discuss the development and evaluation of research-based concept tests for peer instruction as a formative assessment tool in quantum mechanics (QM) courses. The preliminary evaluations show that these tools are effective in helping students develop a good grasp of quantum mechanics.

Surveying Students’ Understanding of Quantum Mechanics

Development of research‐based multiple‐choice tests about quantum mechanics is important for assessing students’ difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non‐relativistic quantum mechanics of one particle in one spatial dimension. We developed a research‐based conceptual multiple‐choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time‐dependence of wavefunction and time‐dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research‐based tutorials and peer‐instruction tool...