Abstract

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.

Highlights

  • Quantum mechanics concepts can be difficult to grasp, especially because many concepts are counterintuitive [1,2,3,4,5,6]

  • In the course of these investigations, we find that many advanced students struggle with these issues related to the time dependence of expectation values

  • Later, when explaining why he didn’t choose statement (2) in question 1 as correct, he stated, “I don’t understand how the fact that the state is in a stationary state is connected to how the expectation value of an observable depends on time

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Summary

Introduction

Quantum mechanics concepts can be difficult to grasp, especially because many concepts are counterintuitive [1,2,3,4,5,6]. We present some results pertaining to the difficulties that first year physics graduate students have with the concept of time dependence of expectation value of operators corresponding to physical observables as manifested by their responses to conceptual multiple-choice questions administered in two different graduate classes.

Results
Conclusion

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