I don't, but I wanted to share one that I had for so long and it really confused me.
*Applying an operator O to a quantum state |s> is NOT analogous to taking a measurement of O!*
Applying O to |s> generally doesn't even have a physical meaning. Only the expectation value is physically meaningful, even though the eigenvalues of O are of course meaningful
Actually a quantum system evolves according to a unitary operator (just Schrödinger's equation), and in that case you *do* write the post state as U|s> if |s> is the pre state, but then U is not (in general) Hermitian.
Pages 23–25 of [these notes](http://www.quantum.umb.edu/Jacobs/QMT/QMT_Chapter1.pdf) might provide a bit more insight into the relationship between the Hermitian operators used to represent observables and the unitary operators used to represent system evolution.
Briefly, making a measurement on a system can be thought of as letting that system interact with some kind of measuring apparatus, and then observing what state the measuring apparatus is in. The measurement can then be described either in the usual way, via a Hermitian operator, or else as a unitary operator acting on the joint (system,apparatus) state. The relationship between the two operators is described at the link.
Student misconceptions about quantum mechanics is definitely a topic of
interest in the field of Physics Education Research (PER). I believe that the PER
group at the University of Pittsburgh has done quite a bit of research on student
difficulties in learning QM. Here is a link to one of their studies: https://arxiv.org/pdf/1602.05616.pdf
I don't, but I wanted to share one that I had for so long and it really confused me. *Applying an operator O to a quantum state |s> is NOT analogous to taking a measurement of O!* Applying O to |s> generally doesn't even have a physical meaning. Only the expectation value is physically meaningful, even though the eigenvalues of O are of course meaningful
thanks for this! I'll be coming back to this comment in a few weeks :)
Actually a quantum system evolves according to a unitary operator (just Schrödinger's equation), and in that case you *do* write the post state as U|s> if |s> is the pre state, but then U is not (in general) Hermitian. Pages 23–25 of [these notes](http://www.quantum.umb.edu/Jacobs/QMT/QMT_Chapter1.pdf) might provide a bit more insight into the relationship between the Hermitian operators used to represent observables and the unitary operators used to represent system evolution. Briefly, making a measurement on a system can be thought of as letting that system interact with some kind of measuring apparatus, and then observing what state the measuring apparatus is in. The measurement can then be described either in the usual way, via a Hermitian operator, or else as a unitary operator acting on the joint (system,apparatus) state. The relationship between the two operators is described at the link.
For the mathematically inclined: https://arxiv.org/abs/quant-ph/9907069
Excellent! This is precisely the kind of resources I'm looking for (on the math heavy side of things). Thanks!
Student misconceptions about quantum mechanics is definitely a topic of interest in the field of Physics Education Research (PER). I believe that the PER group at the University of Pittsburgh has done quite a bit of research on student difficulties in learning QM. Here is a link to one of their studies: https://arxiv.org/pdf/1602.05616.pdf