Good books on quantum mechanics?

[Tail]

I'm searching for good books on quantum mechanics, ones that assume you have close to none prior knowledge and that pretend mathematics doesn't exist (well, at least mathematics mustn't be used in the book...).

Ideas?

Please?

 

[Sonty]

I doubt you can find a book filled only with stories so I'll list my favourites:
1. Sakurai - Modern Quantum dynamics - small, concise and pretty complete
2. Cohen-Tanoudji - great large book (more than 1000 pages)
3. Messiah - smaller than Cohen-Tanoudji, but still 1000+ pages, has also Relativistic QM (Dirac equation)
Of course the big ones contain more stories...

 

[Tail]

Ok, ok, feeling stupid already...


Anyway, could you please tell me how much maths there are in each of the books? I'm sorry, but I CANNOT understand mathematics... I've tried!

 

[plus]

Maybe if you want to get deeply into this, you could get into the philosophy of quantum mechanics rather than into the physics of it. Physics by its very nature is a quantitative subject and needs mathematics in order to express it.

I do not know any books about the philosophy of QM.

 

[Dal]

Quantum Mechanics is truly a subject that shows that our understandings of the language of mathematics is far beyond the expression of language.

 

[Sonty]

The math is the same in all of them. The bigger ones obviously contain more words and less bra-kets per page.

 

[jcsd]

Alstair Rae's "Quantum Mechanics" published by the institue of physicxs is an undergraduate book that starts with the basics yet still manage to introduce chapters on relativistic QM and quantum information.

The thing is though to even start the subject of QM you need a sound mathematical base, quite a few universities wait until the second year of undergraduate degree course until they introduce QM, partly to make sure you have that you are already comforable with the mathematics involved.

 

[Tail]

Hmmm... ok, I'll try to find something and even consider trying mathematics, but then I think I'm a lost cause.


However, my gut feeling is this: if it exists it can be explained non-mathematically. Like all the pretty popular science books that logically explain everything about black holes. I guess I'm not too serious about this (and note that not from an English-speaking country, which means I know few physical and no mathematical terms in English), it just seems very interesting to me.

Anyway, I think that it's possible to explain logically and without mathetmathics how things work, because they DO work.




Ok, if anyone has any new ideas about books... I'd be glad to hear some more suggestions!

 

[selfAdjoint]

May I suggest two books that have almost no math and will give you only a layman's impression of QM, but which in my opinion do that very well? They are The Quantum Code, by Heinz Pagels, and Quantum Reality, by Nick Herbert. Also two books to stay away from if you care about knowing QM at all; The Tao of Physics and The Dancing Wu Li Masters. Both of these are very well written, and they have never been out of print since they appeared back in the age of aquarius. But they will lead you astray and teach you things that aren't so.

 

[qwpoi]

"The thing is though to even start the subject of QM you need a sound mathematical base."


Could you recommend some good books to start building up this mathematical base? I got terribly discouraged by a terrible professor I had freshman year of college and banished math from my mind until recently, when I've become more interested in qm.

 

[Tail]

Thank you SO much, selfAdjoint! The first one you mentioned out of print, but I'm thinking about getting the second one. Hopefully it will allow me to understand QM better!

And I second qwpoi's question, how do I get a "sound mathematical base"?

 

[Sonty]

You need:
1. linear algebra: operator equations, linear (multininear) operators, vector spaces, eigenvalue equations. I know I had an online course, but I can't remember where I got it from. If none pops up, I'll search for it.
2. geometry: coordinate transformations and the representations of operators like &Delta and &Nabla in different coordinate systems (rectangular, polar, spherical, cylindrical, if you want to get abstract elliptical)
3. analysis: differential equations (linear)

 

[qwpoi]

Do you have any specific books to recommend regarding each of these respective topics?

 

[Sonty]

Originally posted by qwpoi
Do you have any specific books to recommend regarding each of these respective topics?

Sorry, a lot of romanian ones. Don't think they are much use to you. Try the Napster https://www.physicsforums.com/showthread.php?s=&threadid=31

 

[selfAdjoint]

Feynmann as a teenager (and his friends too) got up close to the state of the art in their day (Dirac's Principles of Quantum Mechanics - the bible for a generation and a half) by studying the "...For the Practical Man" series (Algebra for the..., Geometry for the..., and he had to wait for it, but eventually Calculus for the...). Last I looked these were still in print, but renamed PC style "for the Practical Worker".

There are a lot of books that take you through high school and lower division undergraduate math. Browse the math and science section of any big book store. Pick the ones that appeal to you best. And follow these rules (or at least feel guilty about not following them)
1) Don't skip. In math everything depends on everything else, and by definition, you don't know how it all hangs together.
2) Do the problems. Or at least the problems you can do. If you get stuck, give thanks you live in the computer age and post it here. Someone will help you.

Set yourself a schedule with each book, not too daring but enough to keep you at it. One section a week? Plug away. Periodically go back to sections you did weeks before and see if you can still do the problems without peeking. This is really stretching your mind, and not everybody can do it. When you're away from your book (like in study hall with nothing to study) run through the latest stuff you've learned in your mind and try to turn it backwards to see if you really understand it.

Best of luck and keep us posted on your progress!

 

[Tail]

There's one thing I don't like about maths when it's combined with physics, though.

In mathematics, you can calculate how everything is, but it generally doesn't give you any answers. How can maths answer the question "why?"?

And it's the only question that is of any interest to me, really...

 

[selfAdjoint]

Insofar as physics answers "why?" at all, it does so through the principles. Such as the principle of relativity, the equivalence pronciple, and the uncertainty principle. These are the things that physicists have found they cannot escape, and which seem basic to the development of physics. A good (and I want to stress GOOD) popular introduction will give you this.

But if after you have read up on Relativity and quantum mechanics you are still unsatisfied, and you want to know why physics is uncertain or relativity is so, rather than something else, then physics has no answer for you. Physics is the study of how nature is, and the study of how she might be is, maybe physics and maybe just speculation.

 

[Tail]

I'm under the impression that all mathematics can offer me is facts, but not explanations. That's why popular science books are enjoyable.

And, if you pick the right ones, they are not incorrect, are they?

 

[selfAdjoint]

Since they can't use math, popular physics books use analogy. And some of their analogies are better than others.

One of the things you need math for is to see how they get those crazy answers. Take two well known things out of quantum physics, the uncertainty principle and "spin-staistics". Both of these come out of deep in the mathematical setup of QM. In fact in order to quantis a theory, they impose commutation laws (the parent of uncertainty) on it.

Spin-statistics refers to the fact that particles with half integer spin (fermions) can't be bound together if they have the sme properties. But particles with integer spins (bosons) like to gather even if they have exactly the same properties. This is a fact of life but it's a theorem in mathematical physics to explain how it happens. It's because of the way their wave functions are.