Surveying students' understanding of quantum mechanics in one spatial dimension

TL;DR

This survey identifies common conceptual difficulties among students learning one-dimensional quantum mechanics and shows that targeted tutorials and peer instruction can improve understanding, highlighting gaps in current graduate courses.

Contribution

The paper develops a conceptual survey for quantum mechanics in one dimension and demonstrates its effectiveness in diagnosing student difficulties and the impact of instructional interventions.

Findings

Students share many misconceptions across undergraduate and graduate levels.

Research-based tutorials significantly improve student understanding.

Graduate courses may not effectively address conceptual understanding.

Abstract

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.