Investigating and improving student understanding of the expectation values of observables in quantum mechanics

@article{Marshman2017InvestigatingAI,
  title={Investigating and improving student understanding of the expectation values of observables in quantum mechanics},
  author={Emily Megan Marshman and Chandralekha Singh},
  journal={European Journal of Physics},
  year={2017},
  volume={38}
}
The expectation value of an observable is an important concept in quantum mechanics since measurement outcomes are, in general, probabilistic and we only have information about the probability distribution of measurement outcomes in a given quantum state of a system. However, we find that upper-level undergraduate and PhD students in physics have both conceptual and procedural difficulties when determining the expectation value of a physical observable in a given quantum state in terms of the… 
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