After Quantum Mechanics: What to Study?

[pierce15]

Hello everyone,

I'm currently trying to figure out what I'm going to study after non-relativistic quantum mechanics. I'm studying from Griffiths's textbook. Here are my questions:

1. Are the first 5 chapters of Griffiths's Quantum Mechanics a suitable background for quantum, or should I read other textbooks as well, e.g. Shankar?

2. Are chapters 6 and beyond in Griffiths, which compose the "Applications" section, worth reading?

3. If the answer to question 1 is "yes," what is the next logical progression, assuming I want to continue on the quantum track? Would it be quantum field theory?

4. If so, what are some good books for self-studying? (I have Zee's Quantum Field Theory in a Nutshell, I'm not sure if it's any good.)

 

[porcupine137]

Hello everyone,

I'm currently trying to figure out what I'm going to study after non-relativistic quantum mechanics. I'm studying from Griffiths's textbook. Here are my questions:

What have you covered so far aside from the start of Griffith's QM? It's hard to suggest much without knowing more, although I will suggest stuff anyway hah.

1. Are the first 5 chapters of Griffiths's Quantum Mechanics a suitable background for quantum, or should I read other textbooks as well, e.g. Shankar?

More, more, more. Shankar. Sakurai (after the first few chapters the quality drops off a fair bit, those chapters were just based on his rough outlines and put together by someone else, but it shows, in full, all the basic stuff you really need to, at a min, get down well first and the early chapters are pretty decent).

First 5 of Griffiths are just an intro, and it barely even does much with the bra-ket side of things.
Especially since you talk about wanting to get into QFT. At least get through a full year of grad school QM first.

2. Are chapters 6 and beyond in Griffiths, which compose the "Applications" section, worth reading?

Not all, but certainly good chunks of that are good to know whatever book you get that stuff from and some of it is very much applied later on (especially, from what I recall the first and last parts of the post ch 5 section of the book).

3. If the answer to question 1 is "yes," what is the next logical progression, assuming I want to continue on the quantum track? Would it be quantum field theory?

My first though would be "no, no" hah.

first a lot more QM and make sure you have a solid bit of EM and CM and all down too

in some ways GR can be an easier next big step to go into than QFT and you'd be well and familiar with tensors and such after that, although you don't have to do that first


Zwieback's Intro to String Theory would be an easier next step I think than a serious QFT book.

A serious QFT book will make what you have looked at so far seem like child's play.

4. If so, what are some good books for self-studying? (I have Zee's Quantum Field Theory in a Nutshell, I'm not sure if it's any good.)

That would be one heck of a leap from the first 5 chapters of Griffiths! Yikes! Assuming you have done intro physics 1-3 plus 5 chapters of Griffiths and that's all she wrote, if you can go from that, and then of all books, dive straight into Zee and make nice progress and get it all and go right along... then wow more power to you. Anyway, you have the book start reading a bit and I'd bet you'll be like ummmm. But if not, hey, wow more power to you. QFT is kinda trick to leap right into next and many find that a difficult book to be a first introduction to Quantum Field Theory on top.

To me a serious full-on grad level String Theory book is the toughest and then next a serious QFT book.

For QFT you might use mixes of stuff like:
Srednicki (an interesting, decent and serious way to begin), Zee (seems tricky as an only or main book, more like a really cool thing once you have sort of partly learned it a bit already), Peskin&Shroeder (an old standard but is a bit typical grad school level booky; a mix of this and Srednicki can be a good start), Hatfield (another unusual entry point, does talk over some things that might get lost in the typical books), Klauber (some say this can be a very good way to get going), Schwartz QFT& the Standard Model (apparently gets some very good things said about it maybe good to start too), there are the Weinberg books (kinda tricky going and would be very rough place to start out and use alone IMO)

I haven't had a chance to dig into the last three yet or even all that much of Zee yet.
I've had a sort of some of Srednicki and some of Peskin&Schroeder class so far.

 

[ZombieFeynman]

I would suggest seeing Griffiths through to completion. You may find it wise to supplement it with Merzbacher or Shankar (which complement each other nicely themselves). I do not think the typical student is well prepared to move on to QFT after chapter 5 of Griffiths (or after finishing the book).

Personally, even after a year of undergraduate quantum mechanics covering Griffiths and a year of undergraduate quantum mechanics covering Merzbacher/Shankar, I still felt like I had holes in my QM knowledge. It wasn't until after qualifiers when I really reviewed it comprehensively did I feel like I mastered it.

 

[bhobba]

AFTER (you should complete Griffiths) THE book to get is Ballentine:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

Beyond that really depends on your interests. I personally went for learning more about decoherence:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

 

[jtbell]

a year of undergraduate quantum mechanics covering Merzbacher/Shankar

My two-semester grad school QM course used Merzbacher. This was followed by a semester that used Sakurai's Relativistic Quantum Mechanics and material from both volumes of Bjorken & Drell's Relativistic Quantum Mechanics and Relativistic Quantum Fields. (This was in 1976, when electroweak theory and QCD were still new and therefore not found in the regular courses yet, just in summer-school lecture notes etc.)

 

[pierce15]

Thanks for all the feedback, everyone. Anyone second Ballentine? How about Shankar? Sakurai?

 

[Demystifier]

Thanks for all the feedback, everyone. Anyone second Ballentine? How about Shankar? Sakurai?

Ballentine is an excellent book, provided that you are interested in a deeper understanding of foundations of quantum mechanics. For that purpose, I also recommend Laloe:
https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

But this does not necessarily mean that these should be your next books to read. Once you learned the basics of quantum mechanics (e.g. from Griffiths), there are actually many different directions for the next step.

Most physicists choose some specific area of physics which USES quantum theory, such as atom and molecular physics, condensed matter physics, quantum optics, nuclear physics, particle physics, or quantum information theory. Those are physicists who want to apply quantum theory to something more concrete.

Or if you prefer to dig deeper in a more abstract direction, you have two possible routs. One route is to study generalizatons of quantum mechanics, such as quantum field theory, quantum gravity, or string theory. The other route is to study foundations of quantum theory.

For each of these choises and sub-choises, there are different recommendations for the "good" books. So the answer to your question ultimately depends on what really do you want.

 

[WannabeNewton]

Thanks for all the feedback, everyone. Anyone second Ballentine? How about Shankar? Sakurai?

If you want to start QFT then what you need to know down cold, second nature, are time-dependent perturbation theory, scattering theory, and the representation theory of rotations/angular momentum. You won't find a better source for this from the books you listed than Sakurai. So I would forget about those other two books. Of the books not listed, Landau Lifshitz QM is the best book on the subject I know of especially when it comes to the topics important for QFT. And the pedigree doesn't hurt either.

Anyways, I think you are getting way ahead of yourself before you even have your foot in the door. If you haven't yet completed Griffiths I wouldn't worry about QFT for a long time. There is a lot of stuff you need to learn in the interim. Have you taken advanced electrodynamics yet? And a math methods course that covers complex methods and Green's functions?

 

[ZombieFeynman]

My two-semester grad school QM course used Merzbacher. This was followed by a semester that used Sakurai's Relativistic Quantum Mechanics and material from both volumes of Bjorken & Drell's Relativistic Quantum Mechanics and Relativistic Quantum Fields. (This was in 1976, when electroweak theory and QCD were still new and therefore not found in the regular courses yet, just in summer-school lecture notes etc.)

Sorry, that was a typo in my original post. I had one year of QM in undergraduate covering griffiths and one year graduate covering Merzbacher/Shankar.

 

[pierce15]

Have you taken advanced electrodynamics yet? And a math methods course that covers complex methods and Green's functions?

I haven't taken advanced electrodynamics yet. By complex methods, I assume you mean complex analysis; I do have experience in this field. I haven't seen Green's functions before.

Once you learned the basics of quantum mechanics (e.g. from Griffiths), there are actually many different directions for the next step.

Most physicists choose some specific area of physics which USES quantum theory, such as atom and molecular physics, condensed matter physics, quantum optics, nuclear physics, particle physics, or quantum information theory. Those are physicists who want to apply quantum theory to something more concrete.

It seems like getting to QFT is going to be a lot of work. Are there are any easy extensions of QM? For example, is nuclear physics easy to jump into after learning basic QM? (Preferably something I could understand with my current rudimentary knowledge of QM, but if it really is necessary to go back and learn QM from a more difficult textbook I'll do so.)

 

[WannabeNewton]

I haven't taken advanced electrodynamics yet.

Then you should set your sights on learning classical electrodynamics as deeply as possible. Learning QFT is literally impossible without a solid grasp of classical EM. In fact this is true of most advanced physics in one way or another.

 

[ZombieFeynman]

I haven't taken advanced electrodynamics yet. By complex methods, I assume you mean complex analysis; I do have experience in this field. I haven't seen Green's functions before.




It seems like getting to QFT is going to be a lot of work. Are there are any easy extensions of QM? For example, is nuclear physics easy to jump into after learning basic QM? (Preferably something I could understand with my current rudimentary knowledge of QM, but if it really is necessary to go back and learn QM from a more difficult textbook I'll do so.)

You might be interested in a solid state physics text or an atomic physics text. I recommend Kittel and Foot respectively for an undergrad.

https://www.amazon.com/dp/047141526X/?tag=pfamazon01-20

https://www.amazon.com/dp/0198506961/?tag=pfamazon01-20

 

[porcupine137]

Thanks for all the feedback, everyone. Anyone second Ballentine? How about Shankar? Sakurai?

Yeah Ballantine is good too I was just going to bring that one up too. Make sure you know all the Balantine/Shankar/Sakurai (non-relativistic book) first. Those three should get you set well.

 

[porcupine137]

My two-semester grad school QM course used Merzbacher. This was followed by a semester that used Sakurai's Relativistic Quantum Mechanics and material from both volumes of Bjorken & Drell's Relativistic Quantum Mechanics and Relativistic Quantum Fields. (This was in 1976, when electroweak theory and QCD were still new and therefore not found in the regular courses yet, just in summer-school lecture notes etc.)

Those are older books, written it that old grad school style, and in some cases having some older points of view although there are some good bits about them. The more recent QFT books can be easier to swallow and present more recent advances and ways of looking at things. (although it is true, that many of them might also leave you without knowing a few practical basics and connections to certain real world phenomenon that were of great importance)

 

[porcupine137]

I haven't taken advanced electrodynamics yet. By complex methods, I assume you mean complex analysis; I do have experience in this field. I haven't seen Green's functions before.

That is very good.

residues, analytic continuation, contour integrals and such all come to play

It seems like getting to QFT is going to be a lot of work. Are there are any easy extensions of QM? For example, is nuclear physics easy to jump into after learning basic QM? (Preferably something I could understand with my current rudimentary knowledge of QM, but if it really is necessary to go back and learn QM from a more difficult textbook I'll do so.)

It depends how deep you want to go. If by nuclear physics you mean you want to understand the strong and weak forces at the deepest level and really work with them then you are back to the same problems again, only maybe even worse. OTOH that often isn't quite what is meant by that and if you really want to get to QFT and such that stuff might just be a detour and you'd be better just getting the rest of QM down, advanced CM down (if not already) and advanced EM down and then you can go to do all the QFT/String Theory/whatnot (if you want something before that, as I said, you might want to hit GR up rather than going into condensed matter or nuclear physics or solid state and such and, at the deepest levels, condensed matter and nuclear could make use of QFT skills).

I'd finish QM up, then do advanced EM or advanced CM next (whatever order you feel like).
Then you could maybe do something like the Zwieback string theory book (if that floats your boat) or maybe go through GR (I could be judging you wrong, but it seems to me that most who bring up QFT tend to get more excited by classes like GR than say solid state physics and such). And then QFT. Although you could do QFT before the stuff in that last sentence.

 

[pierce15]

I'd finish QM up, then do advanced EM or advanced CM next (whatever order you feel like).
Then you could maybe do something like the Zwieback string theory book (if that floats your boat) or maybe go through GR (I could be judging you wrong, but it seems to me that most who bring up QFT tend to get more excited by classes like GR than say solid state physics and such). And then QFT. Although you could do QFT before the stuff in that last sentence.

I guess I'll take this route. Thanks a lot!

 

[Demystifier]

Are there are any easy extensions of QM? For example, is nuclear physics easy to jump into after learning basic QM? (Preferably something I could understand with my current rudimentary knowledge of QM, but if it really is necessary to go back and learn QM from a more difficult textbook I'll do so.)

Yes, nuclear physics (and most other branches of physics) can be jumped into after learning basic QM. Of course, for a deeper insight to any of these branches you will eventually need quantum field theory, but for a start quantum field theory is not necessary.