PHYS771 Lecture 9: Quantum

The cat book again! It seems everyone recommends Griffiths. I finally gave in and my copy should be arriving in a couple weeks.

I've looked through the Feynman lectures a bit, and although it's very nice for a free resource, it doesn't seem to be used very much at all in curriculums.

what are the challengers? there are a few twitter scientists who have written QM textbooks that haven’t made their way into university curriculum yet

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

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.

This is very well written. I checked for a couple of common issues that arise in introductory presentations of quantum mechanics, and found that you navigated most of them correctly.

For example, in the entanglement section, you did discuss that entanglement is a basis independent property, which is a critical point to make - basis dependent "entanglement" exists in classical systems; it is just correlation.

However, I disagree with the inclusion of the paragraph starting "There is something strange about the EPR state." The emphasis on 'immediately' in conjunction with the large distance between Alice and Bob is particularly problematic. The setting of EPR experiments is necessarily in a relativistic world, and in that world time is only a local property. Saying things happen simultaneously (= immediately) implies the presence of a privileged frame of reference, which is exactly what we don't want to do. There are ways of saying these things correctly, but that requires a lot more setup.

I also have a minor nitpick in the sentence below" "We have complete certainty about the state of the composite system |\psi_-\rangle^{AB} , and complete uncertainty about the states of the individual subsystems controlled by Alice and Bob" Since, entanglement exists on a scale, it is better to delete the second "complete" in the sentence, as we can have only partial uncertainty (in the sense of some entanglement measure) about Alice and Bob's systems.

Your books are indeed excellent!

I was wondering... what's your opinion on Geometric Algebra? (If you have one)

i read your book cover to cover it was amazing

edit: https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...