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

Investigating Student Difficulties with Time dependence of Expectation Values in Quantum Mechanics