QM Texts
I've been studying quantum for my quals. It is my nth time around reading Sakurai's book and some sections s have been read n+m_s times :-). Sakurai's Modern Quantum Mechanics is a great book... as long as you are a graduate student, have had QM before and (if it is your first time reading it) have plenty of other books to read alongside it. What makes it good is its approach to quantum theory. What makes it bad is that Sakurai seems to assume that you have some kind of intuition about this stuff and fails to provide explanations sometimes. This is fine if it is your nth time around, but not for newcomers -- even having had undergrad QM.
The usual approach in most texts (like Messiah, Griffiths, Shankar) is some variation of:
what's wrong with classical physics => old quantum theory => modern QM => the cool stuff of quantum theory
Sakurai's is more like:
the cool stuff of quantum theory => modern QM with a hint of what's to come if you keep going in physics (I think... I haven't kept going, yet :-)
I think this is the right way to go about it, not just for a graduate student, but for an undergrad as well. Let me expand on what I mean:
When I was an undergrad, we used Griffiths. The book was good (as should be expected after reading his E&M book). It takes the 'brute force' way into quantum mechanics: PDEs, wave functions, lots of messy integrals and the like. Those are all necessary evils; however, I believe Feynman said that he thought the whole PDE-approach to QM was not really necessary to gain insight into the fundamentals. I think he meant: start with the formalism and the simplest example of it! You don't need PDEs, those just come when your matrix representations of operators become infinite dimensional. And sure, you need to get there at some point, but at heart all you really need to understand the trickery is a spin 1/2 system and its 2x2 matrices. You can even get to Schrodinger's equation using only operators and algebra. I like to call the later this the 'algebraic' approach to QM. Instead of solving PDEs you play with commutators and construct "helper" operators to get to the eigenvalues and eigenstates you are interested in and so forth. This is precisely what Sakurai does and it is fantastic.
There is a couple of sections in Sakurai that seem to be misplaced: the 'stat mech' section in the middle of the 'angular momentum' chapter, and the one about Bell Inequalities in the same chapter. I think they should both be in their own (short) chapters. This is, of course, no real problem, just something to be aware of. The more important problem is that the text is unaccessible to an undergrad and I'll say why at the very end.
Since last year I have been thinking about writing a set of 'notes' to go alongside with Sakurai in an attempt to make it suitable for an undergrad's first-time around. If I pass the quantum qual and take QFT, that may have to wait til summer ;-), otherwise I'll do it as I go through the class here.
Shankar's book is also excellent. Specially the Math and Classical Mechanics reviews that are at the beginning. Nobody should attept to study QM without having spent some time reviewing this material and having it become second nature. I also like that Shankar is very clear (more so than Sakurai), explains things quite a bit (again, more so than Sakurai) and that has the exersies mixed-in with the text. With Sakurai it takes a bit of work to figure out when it is your time to try the next problem from the end of the chapter, but that's very minor as well.
Like I said before, Griffiths is also very good, specially when you get into the situation where you follow the math but have lost "the picture". He also includes a Math review in chapter 3 albeit not as good as Shankar's.
Now, on to why my 'notes' for Sakurai seem to be a good project and why I think it is important that we teach QM this way. The way we teach Physics needs to evolve according to what is relevant in current research. Sure there is a lot to be gained by following the historical path, or by following the messier but conceptually more familiar path (PDE-approach). But, there is much more to be gained by following the conceptual approach that exposes the fundamentals of the theory as...hmmm...well...fundamental. Afterall, the point of science education is producing new scientists, not so much producing new science historians!
Here are the QM books that sit on my bookshelf:
Sakurai
Griffiths
Shankar
Messiah (a true bargain compared to the others!)
The usual approach in most texts (like Messiah, Griffiths, Shankar) is some variation of:
what's wrong with classical physics => old quantum theory => modern QM => the cool stuff of quantum theory
Sakurai's is more like:
the cool stuff of quantum theory => modern QM with a hint of what's to come if you keep going in physics (I think... I haven't kept going, yet :-)
I think this is the right way to go about it, not just for a graduate student, but for an undergrad as well. Let me expand on what I mean:
When I was an undergrad, we used Griffiths. The book was good (as should be expected after reading his E&M book). It takes the 'brute force' way into quantum mechanics: PDEs, wave functions, lots of messy integrals and the like. Those are all necessary evils; however, I believe Feynman said that he thought the whole PDE-approach to QM was not really necessary to gain insight into the fundamentals. I think he meant: start with the formalism and the simplest example of it! You don't need PDEs, those just come when your matrix representations of operators become infinite dimensional. And sure, you need to get there at some point, but at heart all you really need to understand the trickery is a spin 1/2 system and its 2x2 matrices. You can even get to Schrodinger's equation using only operators and algebra. I like to call the later this the 'algebraic' approach to QM. Instead of solving PDEs you play with commutators and construct "helper" operators to get to the eigenvalues and eigenstates you are interested in and so forth. This is precisely what Sakurai does and it is fantastic.
There is a couple of sections in Sakurai that seem to be misplaced: the 'stat mech' section in the middle of the 'angular momentum' chapter, and the one about Bell Inequalities in the same chapter. I think they should both be in their own (short) chapters. This is, of course, no real problem, just something to be aware of. The more important problem is that the text is unaccessible to an undergrad and I'll say why at the very end.
Since last year I have been thinking about writing a set of 'notes' to go alongside with Sakurai in an attempt to make it suitable for an undergrad's first-time around. If I pass the quantum qual and take QFT, that may have to wait til summer ;-), otherwise I'll do it as I go through the class here.
Shankar's book is also excellent. Specially the Math and Classical Mechanics reviews that are at the beginning. Nobody should attept to study QM without having spent some time reviewing this material and having it become second nature. I also like that Shankar is very clear (more so than Sakurai), explains things quite a bit (again, more so than Sakurai) and that has the exersies mixed-in with the text. With Sakurai it takes a bit of work to figure out when it is your time to try the next problem from the end of the chapter, but that's very minor as well.
Like I said before, Griffiths is also very good, specially when you get into the situation where you follow the math but have lost "the picture". He also includes a Math review in chapter 3 albeit not as good as Shankar's.
Now, on to why my 'notes' for Sakurai seem to be a good project and why I think it is important that we teach QM this way. The way we teach Physics needs to evolve according to what is relevant in current research. Sure there is a lot to be gained by following the historical path, or by following the messier but conceptually more familiar path (PDE-approach). But, there is much more to be gained by following the conceptual approach that exposes the fundamentals of the theory as...hmmm...well...fundamental. Afterall, the point of science education is producing new scientists, not so much producing new science historians!
Here are the QM books that sit on my bookshelf:
Sakurai
Griffiths
Shankar
Messiah (a true bargain compared to the others!)
posted by rz at 5:19 PM
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