Lectures on quantum theory, by Chris Isham

[Fredrik]

This is an excellent book, so I'm surprised it's only been mentioned once before in the science book forum. It deserves a lot more attention than that, so I thought I'd at least post a recommendation. The full title is "Lectures on quantum theory: mathematical and structural foundations". If you have already taken a QM class and want to understand the foundations better, this is a very good place to start.

This is supposed to be a fairly easy book, so he has chosen not to include the difficult mathematics (advanced functional analysis, how to find irreducible representations of symmetry groups, etc.). But he always let's you know what he's leaving out, so that you know what to look for if you want to know more. It's written for undergraduates, but I'm sure a lot of graduate students would find it useful too.

It contains a very good discussion about state preparation and measurements, and about some of the interpretational issues. He doesn't go into detail about the various attempts to interpret state vectors as representing objective properties of physical systems, but he talks a lot about "realism" vs "anti-realism". The book also contains an introduction to quantum logic at the end.

It contains a small number of exercises, with complete solutions.

 

[George Jones]

I love this book.

In my head, I referred to this book in quite a few responses to posts in this forum, but, unfortunately, only one response made it from my head to the keyboard.

 

[peterphys]

With reference to fourth anti-realist interpo in section 5.1.1:
... a quantum state should not be associated with an individual system; rather, it
refers only to a collection, or ‘ensemble’ copies of the system...
How to represent this ensemble of system matematically?
Doesn't |psi> represent an individual system?

 

[Fredrik]

That's also possible. (It's option #1 on the list). We don't know what the state vector actually represents, since experiments can only tell us how accurate the theory's predictions are. The predictions are the same regardless of which option on the list is correct.

If we choose option 1, the many-worlds interpretation or something very much like it appears inevitable, because the formalism doesn't contain any indication that one of the possibilities is more real than the others. If we choose option 4, we're essentially saying that even though QM makes excellent predictions about probabilities of results of experiments, it isn't telling us anything about what actually happens to physical systems. It's just a set of rules that tells us how to calculate probabilities of possibilities.