Paul J. Emigh

Student understanding of the measurable effects of relative phases in superposition states

Quantum states have complex probability amplitudes that are sometimes represented by positive real numbers multiplied by complex exponentials. Although the overall phase of a superposition state does not affect the probabilities, the relative phases between the component basis states can have measurable effects. A thorough grasp of relative phase is needed for students to understand various key ideas in quantum mechanics, including quantum interference and time dependence. We present preliminary results from an investigation into student understanding of the measurable effects of relative phases that was conducted in sophomoreand junior-level quantum mechanics courses at the University of Washington (UW). The findings suggest that many students do not recognize that relative phases have measureable effects and tend to overlook the important role that complex numbers play in quantum mechanics.

Student Understanding of Superposition: Vectors and Wave Functions

As part of a broad investigation of student understanding in physics, we have examined student ability with superposition throughout introductory and upper-division courses in physics. This research has focused on examining student ability to add and subtract vector quantities and the wave functions associated with quantum physics. We present results from a series of research tasks designed to probe student understanding of superposition in each of these contexts at various points in undergraduate instruction. In addition, we describe and discuss certain patterns in student reasoning that have been identified across the different tasks, contexts, and courses.