1. Dec 28, 2013

### ilikescience94

I have a pretty basic understanding of the workings of quantum mechanics, and would like to go more in depth by learning the formulas, applications, etc. What would be the best book/lecture course/ online resource you guys know of in which I could better understand QED, QCD, and QM in general?

2. Dec 28, 2013

### R136a1

There are many books out there which are very good. For example, Galindo & Pascual, Hall, Zettili, Griffiths, Sakurai,...

Basically, anything but Ballentine should be good for you.

3. Dec 28, 2013

### atyy

The most important concept for field theory that isn't always evident in textbooks is the Wilsonian viewpoint, which explains why renormalization is not a bizarre process of subtracting infinities.
http://quantumfrontiers.com/2013/06/18/we-are-all-wilsonians-now/

Historically, the Wilsonian insight came from investigating critical phenomena in classical statistical mechanics, which is mathematically analogous to the path integral formulation of quantum field theory. I still find that this a nice way to learn the Wilsonian viewpoint.
http://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2008/lecture-notes/ [Broken]

The other thing I wish were in standard texts is the Osterwalder-Schrader conditions, which tell you why a quantum field theory (with Hamiltonian and Hilbert Space) can be formulated as a statistical theory in Euclidean space. When you see a "Wick rotation" in standard texts, they are making use of this ability to rotate into Euclidean space, calculate there, and then rotate back.
http://www.einstein-online.info/spotlights/path_integrals

Other than that, any textbook is good, eg. Mandl and Shaw, or Srednicki.

Free notes online:
http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf
http://www.damtp.cam.ac.uk/user/dt281/qft.html
http://web.physics.ucsb.edu/~mark/qft.html
http://www.solvayinstitutes.be/events/doctoral/Bilal.pdf [Broken]

Last edited by a moderator: May 6, 2017
4. Dec 28, 2013

### R136a1

Maybe you need to tell us first what mathematics you know? Are you comfortable with calculus? Diff eq? LA?

5. Dec 28, 2013

### dextercioby

Nice comment. Please, see the link to the (fortunately free) research article: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103858969

6. Dec 28, 2013

### WannabeNewton

What's wrong with Ballentine

7. Dec 28, 2013

### R136a1

It's an horrible book. Simply horrible.

First, it tries to be mathematically rigorous and totally botches the job so it confuses people even more. It mentions there's a difference between self-adjoint and hermitian, but then later totally ignores the difference. It spends a paragraph on rigged hilbert spaces but they sadly don't show up later where they can be actually useful. His approach of the spectral theorem suffers the same defects. Why confuse readers with mathematical rigor if he isn't going to be rigorous in the sequel anyway?? He actually does things like "assume this is continuous, let's take the power series expansion". This is fine for QM books which don't claim to be rigorous, but ballentine tries to be rigorous.

Second, his exercises are way too easy. And they are way too unphysical.

He also spends way too much time on the ensemble interpretation, which is totally useless and outdated. Just teach how to calculate stuff and leave the interpretations to philosophy books.

8. Dec 28, 2013

### TumblingDice

Hey here WbN! I was hoping you'd catch this, only because I've been preparing to pick up Ballentine based on the good things I've read here on PF. Now I will sit back and watch posts to get a better idea.

9. Dec 28, 2013

### strangerep

No, he doesn't. He tries to give more background on certain math topics than many other QM books when dealing with unbounded operators, but only to a level that facilitates practical QM calculations. He doesn't pretend to be writing a "QM for Mathematicians" book.

Sure, totally rigorous books on QM are fine and have a valid place in the world. That doesn't make Ballentine "horrible", any more than a non-smoking restaurant is "horrible" because you're not allowed to smoke there.

I was not confused. Were you?

Precisely where in Ballentine do you think explicit mention of RHS could "actually be useful"?

Because his main purpose is to motivate a Dirac-style spectral decomposition for unbounded operators and continuous spectra. Such things handled either by a version of the spectral theorem for unbounded operators in Hilbert space, or by the Gel'fand-Maurin spectral theorem in rigged Hilbert space, and Ballentine describes both, albeit briefly. He's not trying to write a book on functional analysis.

Huh? Focussing on the minimal statistical interpretation, and deprecating Copenhagen, is a modern approach. It's as close as you can get to "shut up and calculate" and therefore is "totally useful" in the practical sense.

"How to calculate stuff" is Ballentine's main emphasis. Sure, he mentions some interpretation-related stuff, but that's intended to help dispel long-standing myths that tend to hang around and confuse students in the modern era.

I agree with that, and sense that Ballentine may be above ilikescience94's current math background. But in that case, so are lots of other books.

10. Dec 28, 2013

### R136a1

Last edited by a moderator: May 6, 2017
11. Dec 29, 2013

### vanhees71

If you want to learn quantum mechanics for physicists, you should indeed not aim at too much mathematical rigor in the beginning. Of course, one must be aware of some subtle issues, and often the physicist's language can be confusing.

So in most physicist's textbooks, they talk about "momentum eigenstates" for particles (usually starting with one-dimensional problems, i.e., for a particle on the entire Euclidean line $\mathbb{R}$). One should tell students early enough that these are not true eigenstates but "generalized eigenstates", because the corresponding wave function (working in position space) are not square integrable. They are in fact distributions on a dense subspace of the appropriate Hilbert space $L^2[\mathbb{R}]$ and can never describe a particle's actual (pure) quantum state!

Then often they talk about a momentum operator for a particle in an infinitely deep potential pot, i.e., for particles restricted to a finite interval although there is no such thing (but the standard Hamiltonian exists on the corresponding Hilbert space).

It's a pretty delicate issue to find the right balance between enough rigor and useful sloppyness, because the main issue in a QM 1 lecture is to comprehend the physics, which is very different from classical physics. I haven't taught QM 1 yet, only QM 2. So I can't say, whether I have the right idea about this balance.

I still think that a very good example for an introductory textbook is

J. J. Sakurai, Modern Quantum Mechanics

I know the 2nd edition, which covers a lot of things on a nice level. A good thing is that it doesn't overemphasize "wave mechanics" too much, although it's of course a strong tool to solve practical problems. Another good intro is also vol. 3 of the Theory Course by Landau and Lifshitz, although they are starting with wave mechanics and don't treat the representation free formalism enough. Another good read is vol. 3 of the Feynman lectures.

Ballentine is an excellent textbook to read further. It goes in some depth concerning the interpretation issue without drifting off to too much "cargo-cult philosophy". The minimal statstical (ensemble) interpretation is, in fact, the interpretation that should be taught first. The interpretational problems and different interpretations of course must be mentioned and discussed, and that Ballentine also does to a certain extent. However, I think that's a topic that should be treated at the very end of QM 1, not in the beginning. QM in the minimal interpretation is disturbing enough!

I'm not an expert in the mathematically rigorous foundations of quantum mechanics. I know that for non-relativistic QT with a fixed number of particles that can indeed be done. I think that the modern approach via the rigged-Hilbert space formalism is easier to comprehend and closer to the way physicists treat the theory. For this, I found the two-volume book by Galindo and Pascual a nice read.

12. Dec 29, 2013

### Staff: Mentor

That would be very much a minority view.

I learnt QM from Dirac and Von-Neumann.

Von Neumann is mathematically rigorous and Dirac - well not - but is what physicists use.

IMHO Ballentine strikes a nice balance between the two approaches and actually explains how the usual approach can be made rigorous by Rigged Hilbert spaces.

Not only that but he develops it from just two axioms, and Schrodingers equation etc is given its correct basis - symmetry.

Its simply the finest book on QM I have ever read and had a BIG effect on me.

I cant recommend it highly enough.

I see it was retracted and replaced by QM Dymystified.

I have the book - and yes - its a bit hodge-podgy. But at the beginning level I don't mind that prior to moving onto something like Ballentine. Its also a good exercise going back through a book like that from the more advanced perceptive of Ballentine and seeing whats going on.

Also Strangereps and Vanhees replies are both spot on.

Regardless of if you finally ascribe to the minimalist statistical interpretation or not (also called the Ensemble interpretation) without a doubt, IMHO, as Vanhees mentions, its the one you should learn and understand first.

After that if you find your mind wandering in that direction I highly recommend Schlosshauer's textbook on Decoherence - an area not well explored in Ballentine:
https://www.amazon.com/Maximilian-A.-Schlosshauer/e/B001JOSA4Y/ref=ntt_athr_dp_pel_1

With that background you can understand the modern take on interpretations.

Thanks
Bill

Last edited: Dec 29, 2013
13. Dec 29, 2013

### aabottom

Thanks for the good replies. I'm tackling The Feynman Lectures on Physics Volume III: Quantum Mechanics right now.

14. Dec 29, 2013

### ilikescience94

Thanks a bunch guys, it seems the general consensus is Ballantine, so I'm going to go with that it seems, thank you all for the suggestions and resources, I bookmarked them all.

15. Dec 29, 2013

### R136a1

I may have retracted my previous criticism of Ballentine, as it is an excellent book. But I'm not sure if Ballentine is right for you. It's pretty math and physics heavy and if you only know the basics of QM, then I don't think it's the right book for you.

Please tell us what your current knowledge of math and physics is, that way we can judge much more easily whether Ballentine really is the right choice for you!

16. Dec 29, 2013

### Staff: Mentor

Personally I don't think it really matters.

If he finds its a bit advanced then he can instead start with some of the other choices - or even the Dymystified book (yes it has issues - but it's cheap and will prepare you for Ballentine).

After studying that come back to Ballentine - then go through the first book again - its amazing what you learn picking up the stuff in more elementary treatments that are corrected in more advanced approaches. For example elementary treatments often make a big deal of the so called wave-particle duality - but from a more advanced standpoint it's basically a croc of the proverbial. Still we all must start somewhere.

Also - take your time - its not a race - you want to UNDERSTAND it - not simply be able to manipulate equations - although that's also important of course - but not at the expense of understanding.

Thanks
Bill

17. Dec 30, 2013

### atyy

I think one has to be careful with Ballentine. Among his errors are his discussion of the quantum Zeno effect, and the outdated remarks on renormalization. Also, it's unclear whether he accepts wave function collapse or an equivalent postulate in the axioms of quantum mechanics, contrary to almost every other textbook including those by Landau & Lifshitz; Cohen-Tannoudji, Diu & Laloë; Nielsen & Chuang; Benenti, Casati & Strini; Haroche and Raimond. Haroche and Raimond do say that decoherence and partial traces may seem to remove the need for collapse, but they don't because the transition from an improper to proper mixed state is equivalent to collapse. A review article by Schlosshauer, whose book bhobba recommends, also states the same.

18. Dec 30, 2013

### strangerep

This is absolutely right.

ilikescience94: tell us your current educational background. Alternatively, take a look through Ballentine using Amazon's "look inside" feature. You should be able to get a rough idea from that about whether your current math background is adequate, or whether you need something gentler first.

Last edited: Dec 30, 2013
19. Dec 30, 2013

### strangerep

I don't feel we've reached consensus yet on whether his discussion of the quantum Zeno effect contains errors. (I think it doesn't, but that's still an ongoing discussion in another thread.)

To all responders in this thread: please note that the original topic is to suggest a book suitable for member "ilikescience94". Discussion of issues in Ballentine, (and/or denial thereof), therefore probably belongs either in the existing Ballentine Book Thread, or else one of the ongoing threads in the quantum forum.

(BTW, to those who have expressed opinions on Ballentine in this thread, you can vote in the poll in the book thread linked above, if you haven't done so already.)

20. Dec 30, 2013

### ilikescience94

I'm taking calc 2 now, when I say I understand the basics, I mean that I underastand the workings somewhat, and I've worked with a few equations like uncertainty, and a little with the schroedinger, I understand special relativity, and somewhat general. I looked at the Ballentine book, it touched on some things I already knew early on, so I ordered it, are there any other books I should check out that are good for learning say GR, because I only understand some of the concepts and haven't explored all of the depth that GR has, and I am very interested in inflation, so it is somewhat necessary.

21. Dec 30, 2013

### R136a1

If you're currently taking calc 2, then I feel that ballentine is not for you. Try at least to complete calculus, and take LA and differential equations. Then you'll be much more prepared for books like Ballentine.

Regardless, I think it's insane to study QM without knowing LA in the first place. So if I were you, I would focus on that.