At what point should a grad student "understand" QM?

[TomServo]

Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes but I don't *get* it, and reading through a book like Shankar or Sakurai or even Griffiths or McIntyre I see plenty of stuff I never would have thought of.

I realize QM is the work of many dozens if not hundreds of geniuses working over decades to put it in its modern form, but I feel bad that I keep forgetting things I learned two chapters ago or that I don't know how to solve the end of chapter problems without help, etc.

Sorry if this question is asked a lot, I couldn't find an equivalent to it using the search.

 

[e.bar.goum]

Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes but I don't *get* it, and reading through a book like Shankar or Sakurai or even Griffiths or McIntyre I see plenty of stuff I never would have thought of.

I realize QM is the work of many dozens if not hundreds of geniuses working over decades to put it in its modern form, but I feel bad that I keep forgetting things I learned two chapters ago or that I don't know how to solve the end of chapter problems without help, etc.

Sorry if this question is asked a lot, I couldn't find an equivalent to it using the search.

I don't think ever, necessarily. For, oh, 98% of grad students. It's just too broad a subject. Have you seen this? http://matt.might.net/articles/phd-school-in-pictures/

All of QM is in that first orange blob. You need to have some understanding of QM if you're to be a physicist, but you don't need a complete understanding of it. Further, if your PhD is in fluid dynamics, for instance, why bother?

 

[TomServo]

I don't think ever, necessarily. For, oh, 98% of grad students. It's just too broad a subject. Have you seen this? http://matt.might.net/articles/phd-school-in-pictures/

All of QM is in that first orange blob. You need to have some understanding of QM if you're to be a physicist, but you don't need a complete understanding of it. Further, if your PhD is in fluid dynamics, for instance, why bother?

I'm going to be working under a quantum gravity theorist. :/

 

[e.bar.goum]

I'm going to be working under a quantum gravity theorist. :/

Well then I reckon you'll need to know some QM!

But, I still don't think you need to be able to write a book. I think you need to have read a few though. And remember, the people who wrote the book didn't come up with all these ideas either. And they probably thought the same thoughts - that they would never have come up with that idea. That's, well, most of the point of research. Quantum mechanics is about a century old now -- think of all the people who worked on it. And don't make the mistake of calling them "geniuses". Sure, some of them probably were. But a lot of them were plain old physicists. The process of doing research isn't about knowing everything about a subject. It's about working on one small area, and trying to solve that one problem.

Clearly, if you're doing well in your QM courses, you're understanding enough of what your lecturer has decided a first year grad student needs to know. When you start doing research, you'll find that what you need to know is a small subset of what is known. That's when you'll really learn it.

 

[atyy]

Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes but I don't *get* it, and reading through a book like Shankar or Sakurai or even Griffiths or McIntyre I see plenty of stuff I never would have thought of.

Aren't those things you don't get just tricks? QM is just Hilbert space, commutation relations, Hamiltonian, Born rule, just like electrodynamics is Maxwell's equations. I think that is all there is to get (I'm not really qualified to say, since I'm a biologist, but I think I could do every problem in Griffiths or Shankar).

 

[radium]

So for some background, I am finishing my first year as a CMT grad student and took a quantum course based on Sakurai my junior year of undergrad. For me, I find that I am able to understand quantum quite well for my level by understanding how the fundamentals are reflected in the mathematical structure, like the importance of unitarity

In understanding the things with more immediate physical consequences, like the uncertainty principle, I really like Sakurai's picture of selective measurements (I like Sakurai a lot in general). I also really like how he is able to relate things like translation, rotation, and time evolution by imagining an infinitesimal change and then going back to the classical generators.

Understanding the Hamiltonian-Jacobi equation is also very important since this is exactly where QM and CM meet in the classical limit. The fact that the wf can be written in terms of a real number and a phase e^iS is also incredibly important in terms of this limit (stationary phase in path integrals) and topological phenomena like the Aharonov Bohm effect that the QHE among others.

Finally, the importance of symmetry in quantum mechanics is incredibly profound in quantum mechanics, and it is incredibly important to understand the consequences, especially how it leads to degeneracies in the eigenvalue spectrum. Representation theory is also very important.

Also, if you will be working in quantum gravity, haven't you taken QFT? Because many of them at my school will not really talk much to students until the have taken QFT I, II and even string theory.

 

[WannabeNewton]

What do you mean by "understand" anyways? There's a difference between understanding it from the perspective of a working experimentalist or theorist and from the perspective of a student studying a textbook. QM is ridiculously easy to understand in the latter sense; that is, unless you read Weinberg and realize that the man has incredibly profound insights on basically every aspect of the theory that take you days of reading over and over to understand one by one

But it seems you're talking about clever intuitive and computational tricks as opposed to actual concepts?

 

[radium]

I think he means that he wants to gain a deep understanding of QM since that would be required to do research in quantum gravity. In that case, the things I mentioned are all very important in high energy (as well as CMT). But you will most definitely need to not only know QM but also QFT and how to get from one to the other conceptually.

 

[TomServo]

What do you mean by "understand" anyways? There's a difference between understanding it from the perspective of a working experimentalist or theorist and from the perspective of a student studying a textbook. QM is ridiculously easy to understand in the latter sense; that is, unless you read Weinberg and realize that the man has incredibly profound insights on basically every aspect of the theory that take you days of reading over and over to understand one by one

But it seems you're talking about clever intuitive and computational tricks as opposed to actual concepts?

I mean concepts, mainly.

 

[TomServo]

Radium, what text did you use for your graduate QM class?

And I take QFT in the Fall.

 

[atyy]

I mean concepts, mainly.

I assume you have the basic formalism of quantum mechanics? Do you know observables, Hilbert spaces, commutation relation, Hamiltonian, Born's rule - and that the specification of these is all there is to quantum mechanics in the sense that Newton's 3 laws are all of classical physics?

For example, do you know the axioms of quantum mechanics as stated in Eq 2.1 to Eq 2.10 in http://www.theory.caltech.edu/people/preskill/ph229/notes/chap2.pdf?

 

[radium]

I used sakurai for quantum 1 and 2 with Shankar for path integrals and a decoherence from the professor's notes. I used QFT and the standard model for QFT which is a phenomenal book.

 

[TomServo]

I assume you have the basic formalism of quantum mechanics? Do you know observables, Hilbert spaces, commutation relation, Hamiltonian, Born's rule - and that the specification of these is all there is to quantum mechanics in the sense that Newton's 3 laws are all of classical physics?

For example, do you know the axioms of quantum mechanics as stated in Eq 2.1 to Eq 2.10 in http://www.theory.caltech.edu/people/preskill/ph229/notes/chap2.pdf?

I know all of those, but I feel like somebody who can only follow directions to get from one place to another, not like somebody who is looking at a map and sees where everything is and what's happening. I feel like somebody who knows to cook custard in a water bath because the recipe says so, but does not know why.

 

[atyy]

I know all of those, but I feel like somebody who can only follow directions to get from one place to another, not like somebody who is looking at a map and sees where everything is and what's happening. I feel like somebody who knows to cook custard in a water bath because the recipe says so, but does not know why.

Hmmm, but beyond that isn't it just calculational tricks specific to the subfield?

A very beautiful book from a condensed matter point of view, that I would put on the same level as Landau and Lifshitz and Weinberg is Wen's https://www.amazon.com/dp/019922725X/?tag=pfamazon01-20. In a way it's a follow-up to Shankar - both Shankar and Wen are condensed matter theorists. There one sees quantum field theory as a language for treating non-relativistic quantum mechanics of many particles. It is similar to the spirit of lattice gauge theory. It is a little bit different from the language of relativistic quantum field theory, but heuristically (if not yet quantitatively) one can say that the practical relativistic quantum field theories are lattice theories with a very small spacing, so that we cannot see the violation of Lorentz invariance.

 

[atyy]

Oh, I should say I am a bit biased and possibly completely off base - but Wen's book could be a start for quantum gravity. The condensed matter view he provides is a prelude to tensor networks - which are related to the language of LQG, and it is also conjectured to be helpful for understanding the AdS/CFT correspondence in string theory. For example, https://www.perimeterinstitute.ca/research/research-initiatives/tensor-networks/tensor-networks-papers lists LQG papers like those by Dittrich and colleagues, while the Friday, May 8 session of http://simons.berkeley.edu/workshops/schedule/3063 has tensor network talks related to AdS/CFT.

 

[TomServo]

Oh, I should say I am a bit biased and possibly completely off base - but Wen's book could be a start for quantum gravity. The condensed matter view he provides is a prelude to tensor networks - which are related to the language of LQG, and it is also conjectured to be helpful for understanding the AdS/CFT correspondence in string theory. For example, https://www.perimeterinstitute.ca/research/research-initiatives/tensor-networks/tensor-networks-papers lists LQG papers like those by Dittrich and colleagues, while the Friday, May 8 session of http://simons.berkeley.edu/workshops/schedule/3063 has tensor network talks related to AdS/CFT.

Why are you a biologist?

 

[atyy]

Why are you a biologist?

Too stupid to be a physicist (so I just read physics for fun).

 

[TomServo]

Too stupid to be a physicist.

But you know about QM and AdS and tensors and stuff!
What if I'm too stupid to be a physicist? :(

 

[atyy]

But you know about QM and AdS and tensors and stuff!
What if I'm too stupid to be a physicist? :(

At least up to the level of grad QM, I guess that shows that it can't be that difficult if a biologist can do it. As it is said, what one fool can do, any other can.

The AdS and tensor stuff is more recent research, and I am just an amateur. It's like how one might enjoy watching a soccer game, even though one isn't a Messi.

Anyway, since you are getting to do this stuff as a professional or at least semi-professional, why not just enjoy it and stop worrying. (Probably at this point some others should give more relevant opinions than this biologist.)

 

[radium]

Wen's book is absolutely wonderful, but I would not recommend it for someone who hasn't taken two semester of condensed matter at the graduate level. It has some wonderful insights about various topics (especially spin liquids), but he assumes in the text that you have prior knowledge of the subject.

Tensor networks are relevant to AdS-CFT in the context of entanglement. The AdS metric emerges when you are talking about it at different levels in the system in DMRG. This suggests that entanglement can be thought about geometrically.

Wen's greatest breakthrough in the 1990s when he was actually very young was realizing the role of topology in the FQHE and in developing theory for SPT states. They topologically ordered states can be studied using tensor metric states and DMRG. In fact you can prove using these tools that there is no topological order in 1D, you can only have SPT states which are different from topological order since they must be protected by some symmetry. Topologically ordered states are robust against any local perturbation.

 

[Entanglement]

(I'm not really qualified to say, since I'm a biologist, but I think I could do every problem in Griffiths or Shankar).

That's really impressive. [emoji4]