  Quantum mechanics is challenging even for advanced undergraduate and graduate
students. In the Schr\"odinger representation, the wave function evolves in
time according to the time dependent Schr\"odinger equation. The time
dependence of the wave function gives rise to time dependence of the
expectation value of observables. We have been exploring the difficulties that
advanced undergraduate and graduate students have with time dependence of
expectation values in quantum mechanics. We have developed and administered
conceptual free response and multiple-choice questions to students to
investigate these difficulties. We also interviewed 23 students individually
using a think-aloud protocol to obtain a better understanding of the rationale
behind students' written responses. We find that many students struggle with
time dependence of expectation values of observables. We discuss some findings.
