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A comment on PHYS771 Lecture 9: Quantum – Scott Aaronson.

Re:PHYS771 Lecture 9: Quantum – Scott Aaronson by hackandthink on Sunday August 20, 2023 @12:24PM (#37200584)
"The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs"

In my opinion, this is not the most natural and easiest way to get into quantum mechanics.

And there are also (undergraduate) physics books that tackle the quantum mechanical concepts directly, e.g:

https://www.feynmanlectures.caltech.edu/III_toc.html

especially:

https://www.feynmanlectures.caltech.edu/III_03.html (Probability Amplitudes)

Negative probabilities (Wigner Functions) are more advanced:

https://en.wikipedia.org/wiki/Wigner_quasiprobability_distri...

Lucien Hardy "Reconstructing quantum theory" is really conceptional, but I think it is not the best way to start.

https://arxiv.org/abs/1303.1538

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Re:PHYS771 Lecture 9: Quantum – Scott Aaronson by akjssdk on Sunday August 20, 2023 @01:47PM (#37201345)
I am not sure if this is how it is a correct representation. I believe a common approach is to do a short history of quantum in the first year, and then do a from the ground up approach in the second and third year. Depending on who teaches it, this is either starting from a particle in a box or the approach stated here. The historical story is useful, because it tells a little bit of the why.
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Re:PHYS771 Lecture 9: Quantum – Scott Aaronson by eigenket on Sunday August 20, 2023 @02:30PM (#37201747)
Wigner Functions are great and all, but they work quite badly for finite dimensional systems. Specifically they are a bit complicated for odd dimensional systems and don't work at all for even dimensional systems (see e.g. [1]). Given their limited applicability I don't see why we should treat them as particuarly fundamental when introducing quantum mechanics to students.

[1] https://arxiv.org/pdf/quant-ph/0507094.pdf

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