What to learn/read to understand quantum mechanics deeper?

[Gerenuk]

I thought about digging deeper into quantum mechanics to make it more intuitive for me and "figure out the principle". I know university level QM very well. Maybe I should gather more knowledge about relativistic QM though.

What further concepts are at the core of QM (complicating theories, tensor stuff, ...)? Which books are recommended?

I do not wish to learn about all possible approximations and theoretical tools to solve problems, even though only they might make understanding of some phenomena possible. So, only concepts free from approximations.

Also I'd try to exclude thinking about particle physics or gravitational effects. This one "approximation" I can accept.

 

[Minich]

Group theory, group theory representations, Einstein-Podolsky-Rosen gedanken experiment, Bohmian quantum mechanics, canonical transformations...

Quantum measurements...

 

[Gerenuk]

Group theory, group theory representations, Einstein-Podolsky-Rosen gedanken experiment, Bohmian quantum mechanics, canonical transformations...

Do I really need group theory? I mean I'm not trying to prove energy degeneracies.

EPR is probably good to know, but in fact by learning the basics I'm trying to understand EPR. It doesn't have a new ingredient for QM?

Bohmian I should look at, but at first maybe I stick to the conventional method.

I heard something about spinors. Maybe I'll have a look.

 

[George Jones]

I highly recommend "Lectures on Quantum Theory: Mathematical and Structural Foundations" by Chris Isham,

http://www.worldscibooks.com/phy_etextbook/p001/p001_toc.pdf .

 

[Gerenuk]

I searched for some key words.

Maybe as an outview:
Which mathematical concepts are important to understand many-body relativistic QM?

What are group representations and this general spinor stuff useful for?

Does QFT give new insights into QM itself?

What's important to understand photons quantum mechanically?

 

[Fearless]

I have actully been thinking about this also. Does a materials physicist/chemist really need QFT? Or is it only for particle physics etc?

 

[f95toli]

I have actully been thinking about this also. Does a materials physicist/chemist really need QFT? Or is it only for particle physics etc?

It depends. QFT is extensively used in some branches of condensed matter physics (to describe many-body effects). However, unless you are planning to become a theorist working in one of those fields you don't need to know anything about it (you only need to understand the results of those calculations). Hence, most working physicists/chemists don't know much about QFT.
That said, it might still be good to have some idea about what QFT is.

 

[Gerenuk]

It depends. QFT is extensively used in some branches of condensed matter physics (to describe many-body effects). However, unless you are planning to become a theorist working in one of those fields you don't need to know anything about it (you only need to understand the results of those calculations). Hence, most working physicists/chemists don't know much about QFT.
That said, it might still be good to have some idea about what QFT is.

Oh OK. I know the CMP guys here do Green functions and Feynman diagrams, but didn't know they are into QFT. I actually do not want to use these numerical methods, which rely on approximations to deduce results.

But on the other hand I want to know the foundations without any gaps (yet avoid deeper knowledge of too much abstract maths).

For example I cannot stick to just classical QM, because the symmetrization is introduced ad hoc. So I need to include relativistic QM.

In the end I basically want to grasp entanglement. To know what it is and even more important to know what it is not.
And also understand the Schrödinger cat state, i.e. what it means that the superposition of state can have a phase difference.

 

[Minich]

I do not wish to learn about all possible approximations and theoretical tools to solve problems, even though only they might make understanding of some phenomena possible. So, only concepts free from approximations.

So the only output to become a mathematician.

In our University mathematical physics was not considered as physics at all )

 

[las3rjock]

I do not wish to learn about all possible approximations and theoretical tools to solve problems, even though only they might make understanding of some phenomena possible. So, only concepts free from approximations.

If you've already taken university-level quantum mechanics, chances are that you've already solved every approximation-free problem. Off the top of my head, only the particle in free space, (in)finite potential well, rectangular wave potential, harmonic oscillator, hydrogen atom, and maybe one or two others are exactly solvable. Unfortunately, reality tends to be more complicated than these idealized problems (e.g. non-hydrogen atoms are n-body problems, not the idealized two-body hydrogen atom), so approximations are almost inevitably needed to solve nontrivial problems.

As for a book on the foundations of quantum mechanics, I have heard good things about Quantum Theory: Concepts and Methods by Asher Peres. His treatment is said to be uniquely helpful to understanding current research in quantum theory, such as quantum computation and quantum communication.

 

[Fearless]

First of all I would like to point out to the assembled gentlemen and women that I have no idea of what "actully" means. :p

las3rjock: Yeah that is true, but that is why we have perturbation theory. ^^

f95toli: But if we take the question and put it on it's own head, will learning QFT help me in the non-rel QM? Or is it a whole other ballpark?

Gerenuk: Greensfunctions is something on my list to teach myself or look for in some related course to physics/maths. so in my view I don't really see the problem in doing greens functions or feynman diagrams (the penguin by the way is hilarious).

 

[f95toli]

Well, most (all?) of the QFT used in condensed matter is non-relativistic (maybe with the expection of graphene). QFT is used to describe e.g. Quantum Hall Fluids and similar systems. Hence, QFT is nowadys not nearly as "exotic" as it was a few decades ago. So whether or not it will help you depends on what kind of physics you are interested in; QM is a HUGE topic and it is not possible for single person to know all of it.

If you are interested in how QFT is used on condensed matter I would suggest you take a look at "Quantum Field Theory in a Nutshell" by Zee, there are a few chapters in there about how QFT can be used to describe certain solid state systems.

 

[will.c]

I also recommend Zee, since it's a great general introduction. If you're serious about QFT methods in cond-mat, other good books are Nagaosa (though very brief) and Ed Fradkin.