What are you reading now? (STEM only)

[Frabjous]

Historically that may be right, but neither the PE nor Compton scattering prove the necessity for quantization of the em. field.

What demonstrated the necessity of the quantization of the em field?

 

[Demystifier]

Historically that may be right, but neither the PE nor Compton scattering prove the necessity for quantization of the em. field. This is really well-known now. Why do textbook writers, particularly of QM intro textbooks, always just copy the mistakes from the tradition?

Obviously, it's not known well enough.

Besides, where are the postulates clearly stated?

Sec. 5.3.

 

[Demystifier]

What demonstrated the necessity of the quantization of the em field?

Spontaneous emission, I would say.

 

[vanhees71]

What demonstrated the necessity of the quantization of the em field?

E.g., Spontaneous emission and the HOM effect

https://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect

 

[vanhees71]

Obviously, it's not known well enough.Sec. 5.3.

Ok, well. Where can I find an hermitean operator to measure in the lab? Maybe I ask my experimental colleagues on Monday ;-))... Then there's an "instantaneous collapse". The question is, why does one need another 1000+x-page sloppy book on QM? :-((

 

[Demystifier]

Then there's an "instantaneous collapse". The question is, why does one need another 1000+x-page sloppy book on QM? :-((

Who is worried about philosophical quibbles now?

 

[vanhees71]

It's not philosophical. I don't bother too much about the "instantaneous collapse" postulate without even mentioning that it's highly problematic. That you may indeed see as a philosophical detail, I'll never would bother to discuss with beginners in QM, but as far as I could see glancing over the book, it's sloppy also in the math (and thus also in the physics). Admittedly, I have a few points I check to see whether I want to buy a new QM physics book.

(1) How are states defined: the author states its given by the state ket. That's too sloppy for my taste, because it's very important to identify a ray (or equivalently the projection operator $|\psi \rangle \langle \psi|$) with a (pure) state and not $|\psi \rangle$ itself. Without this, there'd be no non-relativistic QM (the unitary representations of the Galilei group don't lead to physically useful quantum theories), no half-integer spin, and many more problems.

(2) The operators representing observables must be essentially self-adjoint; Hermitean is not sufficient. Also one measures not an Hermitean (or self-adjoint) operator in the lab but real-world "objects", but the latter is again maybe a bit philosophical, but I've never understood what people mean when they state they'd measure an abstract mathematical entity like a self-adjoint operator in Hilbert space. I've never seen one around me ;-)).

(3) Is the question, why orbital angular momenta have only integer and not half-integer eigenvalues (properly) addressed? As expected from (1) and (2), of course not. Already Pauli knew in 1925/26 that of course the claim that a wave function must be unique as a classical field is not a valid argument. The lack of realizing this is of course due to the sloppiness with regard to item (1) above.

(4) Is the photon picture used at least qualitatively correct, if it is used at all in a beginners-QM (non-relativistic QM)? The answer is definitely no here too.

 

[andresB]

(2) The operators representing observables must be essentially self-adjoint; Hermitean is not sufficient. Also one measures not an Hermitean (or self-adjoint) operator in the lab but real-world "objects", but the latter is again maybe a bit philosophical, but I've never understood what people mean when they state they'd measure an abstract mathematical entity like a self-adjoint operator in Hilbert space. I've never seen one around me ;-)).

I don't get the claim. It is true that the physically relevant QM representation of the Galilei group is not faithful but projective. Yet, it is a unitary projective representation.

 

[vanhees71]

Sure, but why should you look for projective representations in the first place if the absolute phase of the state ket were physically significant?

 

[Hamiltonian]

@vanhees71 I have seen you dislike most popular intro QM books, eg. Griffths QM and now Zwiebach's new book. What book do you usually recommend to a complete novice?
or do you simply believe there is no one good intro QM book :(

 

[martinbn]

@vanhees71 I have seen you dislike most popular intro QM books, eg. Griffths QM and now Zwiebach's new book. What book do you usually recommend to a complete novice?
or do you simply believe there is no one good intro QM book :(

Laundau Lifshitz

 

[vanhees71]

@vanhees71 I have seen you dislike most popular intro QM books, eg. Griffths QM and now Zwiebach's new book. What book do you usually recommend to a complete novice?
or do you simply believe there is no one good intro QM book :(

Sakurai, Ballentine, Weinberg, Messiah, Landau and Lifschitz vol. 3, Dirac. There are many good into books.

 

[MathematicalPhysicist]

Sakurai, Ballentine, Weinberg, Messiah, Landau and Lifschitz vol. 3, Dirac. There are many good into books.

No list can be complete without Cohen-Tanoudji's books...
P.S
I really should start reading this book, reminds me of Courant-Hilbert or Courant-John in calculus.
I only read parts, and it's good I read Cohen-Tanoudji that once I took an exercise in an undergraduate QM1, there was a question on Glauber something. No one in class knew how to answer this exercise but me, cause I gave a look at the book's index.

Good for me...

 

[Demystifier]

Sakurai, Ballentine, Weinberg, Messiah, Landau and Lifschitz vol. 3, Dirac.

But some of those say that there is collapse.

 

[Demystifier]

HOM effect
https://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect

I've just noticed that this effect is also discussed in the Zwiebach's book, another topic that can rarely be found in other general QM textbooks.

 

[vanhees71]

But some of those say that there is collapse.

Sure, if you look for books, where they don't mention collapse, the list will be very short ;-).

 

[George Jones]

Admittedly, I have a few points I check to see whether I want to buy a new QM physics book. ...

These are interesting criteria. What is the set of books satisfies these four criteria, and also is suitable for a first undergrad quantum mechanics course (beyond Modern Physics) at a typical North American university? It wouldn't surprise if it's the empty set.

 

[haushofer]

For me, no textbook is perfect. I'm happy to get some misrepresentations; basically every book has them and no author is God. I prefer writing style and topic selection. The very first reason I read textbooks is because I'm in love with physics and mathematics, and if an author resonates with that in his writing style, much can be forgiven.

 

[vanhees71]

These are interesting criteria. What is the set of books satisfies these four criteria, and also is suitable for a first undergrad quantum mechanics course (beyond Modern Physics) at a typical North American university? It wouldn't surprise if it's the empty set.

Well, Sakurai is pretty close. My favorite intro textbook is unfortunately not available in English: E. Fick, Einführung in die Grundlagen der Quantentheorie, Aula-Verlag Wiesbaden (1979)

 

[MidgetDwarf]

Well, Sakurai is pretty close. My favorite intro textbook is unfortunately not available in English: E. Fick, Einführung in die Grundlagen der Quantentheorie, Aula-Verlag Wiesbaden (1979)

Someone give Vanhees a large annual salary, so that he can translate German math/physics books!

 

[andresB]

Sure, but why should you look for projective representations in the first place if the absolute phase of the state ket were physically significant?

Do most (all) QM books don't say that? I remember being told from the very beginning by my QM teacher that total phases were irrelevant, so it's not something I actively look at in books, it seems quite obvious.

 

[vanhees71]

That's the point. It's not a very difficult fact that not vectors in Hilbert space but rays represent (pure) states, and you can (and imho should!) teach it from the very beginning, but it's often not stated explicitly in the introductory chapters of newer QM textbooks. In a book like Sakurai it indeed is taught correctly from the very beginning. Also the related issue with the orbital angular momentum is discussed correctly there.

 

[George Jones]

Besides, where are the postulates clearly stated?

Sec. 5.3.

This version of the axioms is given in the I Essentials part of the book. A more sophisticated version of the axioms (for isolated systems) is given in section 16.6, which is in the II Theory part of the book. Here, Zwiebach clearly states "A1. States of the System The complete description of a quantum system is given by a ray in a Hilbert space H." (Zwiebach's bold)

 

[haushofer]

I'm reading The art of statistics by Spiegelhalter now. Fun book which stresses conceptual aspects of statistics and data analysis.

 

[BWV]

Finally an honest math book title

 

[andresB]

Finally an honest math book title
View attachment 301619

Ah, yes. I remember that book. It's the one where you need preliminaries to understand the preliminaries of page 1.

 

[BWV]

Ah, yes. I remember that book. It's the one where you need preliminaries to understand the preliminaries of page 1.

Yes, found the first part easy to follow, then he lost me

 

[Demystifier]

View attachment 301703

In (1), the indices do not match. In (2), the horizontal line of the square root is too short. And I don't see how is 2+3=5 clear, it took several hundred pages to prove 1+1=2 by Whitehead and my avatar.

 

[George Jones]

"Lectures on the Philosophy of Mathematics" by Joel David Hamkins (Professor of Logic and Fellow in Philosophy at Oxford). After 50 pages about numbers (of various kinds) he writes " "I am truly very sorry, but we do not know, fully, what numbers are." He is a very engaging writer.

 

[haushofer]

"Lectures on the Philosophy of Mathematics" by Joel David Hamkins (Professor of Logic and Fellow in Philosophy at Oxford). After 50 pages about numbers (of various kinds) he writes " "I am truly very sorry, but we do not know, fully, what numbers are." He is a very engaging writer.

Maybe you'll also like

Why Beliefs Matter: Reflections on the Nature of Science,

https://www.amazon.nl/dp/0198704992/

then (written by a mathematician)

 

[haushofer]

Finally an honest math book title
View attachment 301619

This is actually how I experience quite some of these math books too, and mostly read mathbooks/notes written by physicists like Tong or Zee nowadays (God knows I tried!). I guess I value intuition more than rigor.

 

[romsofia]

Maybe you'll also like

Why Beliefs Matter: Reflections on the Nature of Science,

https://www.amazon.nl/dp/0198704992/

then (written by a mathematician)

This seems like a fun book, I will probably be getting it. Thanks for mentioning it!

 

[Demystifier]

"Lectures on the Philosophy of Mathematics" by Joel David Hamkins

Thank you for the suggestion, now I'm reading it too.

 

[WWGD]

For me, no textbook is perfect. I'm happy to get some misrepresentations; basically every book has them and no author is God. I prefer writing style and topic selection. The very first reason I read textbooks is because I'm in love with physics and mathematics, and if an author resonates with that in his writing style, much can be forgiven.

Like 'Misrepresentation Theory'?

Thank you for the suggestion, now I'm reading it too.

JDH is a major poster in Math Logic in Math Stack Exchange, maybe in Overflow too. He's one of those monsters with like 500k score, so that maybe you can gleam some of his material from there. I met him once. Cool guy, but seems to have a wolfman thing going. Careful with him after sundown, as the J, H stand for Jekyll and Hyde ;) Joking on the wolfman look. He was very nice0. I read, understood and explained to someone his take on how Compactness in Logic compares to Compactness in Topology like 3 times, and then forgot most of it.

 

[Field physics]

I am reading the principals of fusion energy