Intro Quantum Mechanics Text for the Summer?

[Spatium]

Hey guys I've been thinking for the summer I'd like to get a bit of an introduction to QM. I'll be doing research so something that I can just read through and do some problems every now and then is great.

My math background so far is most of the Calculus sequence (haven't done the vector calculus theorems yet, but I'm going to work on those too), a linear algebra course, and a tiny bit of differential equations.

I've identified Shankar and Griffiths as the typical "classics", and am also interested in Dirac's book (though is much of it irrelevant now with more modern developments? Would I be going in the wrong direction?)

So any particular recommendations? Again I'll be taking a course in QM eventually, just looking for something to keep my mind busy.

 

[atyy]

If you're taking QM eventually, I suggest linear algebra as your self-study project.

Shankar and Griffiths are good. Also Sakurai and Napolitano. Maybe French and Taylor if you're looking for something a little more introductory. I strongly recommend the introductory chapters of Landau and Lifshitz. And the formal presentation in Cohen-Tannoudji, Diu & Laloe.

Dirac is still good, despite the occasional mistake. The founders of the subject got it structurally right, except for the no hidden variables part. The other major conceptual revolution unknown to Dirac was Wilson's renormalization group and effective field theory, but that came after Feynman. In modern times, there is a slight preference for the measurement axioms to be stated using POVMs, although POVMs can be derived from the traditional projective measurements. But the old fashioned way of using projective measurements as axiomatic is not just in Dirac, but also in Shankar, Sakurai & Napolitano, Landau & Lifshitz, and Cohen-Tannoudji, Diu & Laloe.

Try Nielsen and Chuang or Matteo Paris's "The modern tools of quantum mechanics" http://arxiv.org/abs/1110.6815 for the axioms using POVMs.

 

[vanhees71]

Try Nielsen and Chuang or Matteo Paris's "The modern tools of quantum mechanics" http://arxiv.org/abs/1110.6815 for the axioms using POVMs.

Hm, already Postulate 1 is not entirely correct. The correct statement is that a (pure) state is represented by a ray in Hilbert space and not a specific normalized state vector (which is only one possible representant of the state). This is very important since without it there was no non-relativistic quantum theory, because the unitary representations of the (classical) Galilei group do not lead to a physically useful quantum mechanics. You need the central extension of the Gailei group with mass as a non-trivial central charge.

Another argument for the ray definition of states is the existence of spin-1/2 particles, i.e., that not the rotation group SO(3) is the true symmetry group of rotations in nature but its covering group, the SU(2). Also this makes only sense, if you define states as being represented by rays not by normalized state vectors.

In postulate 2 they should have written self-adjoint operators instead of hermitean operators, but that's another story.

 

[jasonRF]

Spatium, may I ask what your physics background is? Have you at least taken a 2 or 3 semester calculus based intro physics sequenc covering mechanics, thermo, E&M and classical waves?

 

[rezeew]

Hello! It's great to hear that you are interested in learning about Quantum Mechanics over the summer. I highly recommend starting with Shankar or Griffiths as they are both well-respected and comprehensive introductions to the subject. They will provide you with a solid foundation in the fundamentals of QM.

In terms of your math background, it sounds like you have a good grasp on the necessary concepts. However, I would suggest brushing up on your linear algebra skills as it is a crucial tool in understanding QM.

As for Dirac's book, it is a classic and definitely worth reading, but keep in mind that it was written in the early 20th century and may not cover some of the more modern developments in QM. However, it is still a valuable resource for understanding the foundations of the subject.

Overall, my advice would be to start with either Shankar or Griffiths and supplement your learning with additional resources such as online lectures or problem sets. And don't be afraid to delve into more advanced topics as you progress. Happy learning!