Developing and assessing tutorials for quantum mechanics: Time dependence and measurements

Tutorials in Physics: Quantum Mechanics is a set of curricular materials for supplementing upper-division quantum mechanics instruction, developed by the physics education group at the University of Washington. We describe the development of a sequence of three tutorials that focused on quantum measurements and time dependence. This sequence of tutorials is based on prominent findings in the research literature related to student understanding, as well as classroom techniques and strategies that have proved effective in other instructional contexts in physics. We also present data from a set of four exam questions used to evaluate how effectively these tutorials improve student ability to use correct mathematical and conceptual reasoning to predict the time evolution of quantum probabilities. We find that student performance on each question is significantly better than on corresponding questions given after only traditional instruction, with effect sizes that range from small to moderate. This improvement, along with a decrease in the prevalence of common incorrect lines of reasoning, supports our claim that this set of three tutorials from Tutorials in Physics: Quantum Mechanics assists advanced undergraduate students’ in developing a conceptual understanding of some of the fundamental quantum concepts about time evolution and measurements when given after traditional lecture instruction. However, our results also show that there are some topics with which many students still struggle and, thus, that there remains room for further research and development of materials for these topics.

Figure 1

Timeline of instruction associated with each tutorial topic.

Figure 2

A pair of questions about the time dependence of position probabilities. The pretest was given after lecture instruction on time dependence but before the tutorials. The post-test was given after the full sequence of three tutorials focusing on quantum measurements and time dependence.

Figure 3

Student performance on question 1, before and after completion of the tutorials. Error bars represent the standard error.

Figure 4

A pair of questions about the time dependence of energy probabilities. The pretest was given after lecture instruction on time dependence but before the tutorials. The post-test was given after the full sequence of tutorials, as part of the same exam as post-test question 1.

Figure 5

Student performance on question 2, before and after completion of the tutorials. Error bars represent the standard error.

Figure 6

Several questions about the effects of measuring position. The pretest was given prior to the final tutorial in the sequence, but after lecture instruction and the first two tutorials. The post-test was given after completion of the full sequence, as part of the same exam as post-tests 1 and 2. The text in the figure has been edited for length.

Figure 7

Student performance on question 3, before and after completion of the tutorials. Error bars represent the standard error.

Figure 8

Student performance on all four post-test questions at three different universities. Error bars represent the standard error.