An investigation of student understanding of classical ideas related to quantum mechanics: Potential energy diagrams and spatial probability density

This dissertation describes the results of two related investigations into introductory student understanding of ideas from classical physics that are key elements of quantum mechanics. One investigation probes the extent to which students are able to interpret and apply potential energy diagrams (i.e., graphs of potential energy versus position). The other probes the extent to which students are able to reason classically about probability and spatial probability density. The results of these investigations revealed significant conceptual and reasoning difficulties that students encounter with these topics. The findings guided the design of instructional materials to address the major problems. Results from post-instructional assessments are presented that illustrate the impact of the curricula on student learning.