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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 the measurable effects of relative phases in superposition states