Advanced Quantum Mechanics Books Suggestions

[saim_]

I have a good enough grasp of basics of QM at the level of Griffiths and Binney. Anyways, I want to start a more advanced book. I have my heart set at starting one of the following

Dirac's "Principles of QM"
John von Neumann's "Mathematical Foundations of QM"
L. Ballentine's "QM: A Modern Development"
Pascual and Galindo's "QM: Vol 1"
Sakurai's "Modern QM"
Landau's "Non-relativistic QM"

Suggestions? I always prefer more mathematical and theoretical approach than calculational approach; no interest in problem solving whatsoever, so please suggest accordingly.

 

[Jorriss]

no interest in problem solving whatsoever, so please suggest accordingly.

... so what do you want then? A book you can just read like a novel?

In any event, I love Sakurai (though I have never used his chapter on scattering, I hear its not very good).

 

[saim_]

... so what do you want then? A book you can just read like a novel?

I didn't mean it so strongly. What I meant is I want a book more along the lines of Dirac and Neumann which develop mathematics and theory more formally and less long the lines of Griffiths, the stated aim of which is teaching how to 'do' QM and cares less about math and theory.

 

[Jorriss]

I didn't mean it so strongly. What I meant is I want a book more along the lines of Dirac and Neumann which develop mathematics and theory more formally and less long the lines of Griffiths, the stated aim of which is teaching how to 'do' QM and cares less about math and theory.

Ahhh, but then, even in pure math classes you learn by doing tons and tons of problems. Do you just mean you meant derivation and 'proof' type problems and not 'A particle is confined to this and this find this and this..?'

Or do you actually just not want to do any problems?

Because, iirc, Sakurai has mostly the former whos problems develop the structure of theory and are, for the most part, insightful.

 

[saim_]

Do you just mean you meant derivative and 'proof' type problems and not 'A particle is confined to this and this find this and this..?'

Exactly what I meant. I can't do calulational stuff unless I have to, like for a course. Derivations and proofs I can do or read all day long :D

 

[deluks917]

Quantum Mechanics for Mathematicians might be interesting.

 

[saim_]

@deluks917: That is a graduate text and that too for math grads. I just went through its table of contents and as much as I love math, I don't know all that much of it :D So I want something that develops the math a little more gently.

 

[bhobba]

I am more of a mathematical physics type guy than a straight physics person and like to see the math.

I have quite a few QM books - Von Neumann, Dirac, Griffiths, etc etc. By far and by a long way Ballentine is the best. For example you get an introduction to Rigged Hilbert Spaces which IMHO is the correct setting for QM rather than Hilbert Spaces. Also the dynamics such as Schroedinger's equation is derived from invariance and not a separate postulate which adds greatly to understanding the actual logical structure of the theory. Basically you understand QM is really a consequence of just 2 postulates and they contain the essential mystery. I believe it can really be reduced to one - the superposition principle - but that is another story.

Thanks
Bill

 

[saim_]

@bhobba: That is just great! That's exactly the kind of book I wanted. Thank you for your help.

 

[Daverz]

One book that's not often mentioned is Arno Bohm's. His mathematics is very precise, but he also covers a lot of physics.

https://www.amazon.com/dp/0387953302/?tag=pfamazon01-20

 

[genericusrnme]

I've read both Sakurai's "Modern QM" and Landau's "Non-relativistic QM". Sakurai's is certainly more modern and the first few chapters are really nice but Landau and Lifgarbagez' book has a certain elegance to it even though a lot of the material in it is a little outdated (it's still good though, it explains the stuff at Griffiths' level but a lot clearer and precice than Griffiths' book which is horrid imo)