Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction. We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function…

Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…

The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…