mathematical physics books, Hassani's or Arfken's.

MathematicalPhysicist

im thinking on buying one of the two books:
1)Mathematical Physics- by sadri hassani.
2)Mathematical Methods For Physicists - by george arfken.
which is the better choice?

siddharth

Have you considerd Mathematical methods in the Physical Sciences by Mary L.Boas? That's an excellent book for reference, with a lot of worked out examples and problems.

maverick280857

I have been reading from Arfken/Weber and Boas and I think a combination of these books (as emphasized in Griffiths' QM) is a good idea. I have no idea about Hassani.

If you are interested in Theoretical Physics per se, there are several books by Joos, Frank/Slater, etc.

MathematicalPhysicist

after you suggested this book, i searched it on amazon, the new edition looks very expensive to me, i guess that the older editions i could borrow at my uni, is it better than arfken's book?

George Jones

Boas is at a lower level than Arfken, but it also more pedagogical.

For what do you want your choice to prepare you?

MathematicalPhysicist

basically the course is called methods in theoretical physics it covers the next topics:
complex functions,fourier theory,Sturm-Liouville theory, partial differential equations,green functions,legendre functions,bessel functions,gamma function,special functions,hypergeometry,WKB method and group theory.
(there are more topics).
ive looked in amazon at both the books i stated above, and i reackon they cover the same material, so which covers it better?

George Jones

Sometimes, it is difficult to say that one book is better the other. Your course seem to cover what I would call classical mathematical physics. Both books cover classical mathematical physics, but it seems that Hassani covers a little more of what I would call modern mathematical physics. This may just be extraneous stuff for you. Also, I am unfamiliar with just how good Hassani's style of presentation is.

MathematicalPhysicist

what topics would you consider as modern mathematical physics?

matt grime

Yes, from the titles, those two books appear to be doing entirely different things. Arfken is a very well respected book for engineers and physicists - a good discourse on things like tensors.

Mathematical physics, at least to me, is things like string theory, QFT, TQFT, CQFT, and comes from an entirely different direction.

The book by Hassani above bears no relation to this view of mathematical physics.

Try reading Jon Baez's this weeks finds in mathematical physics.

hazem

Arfken is the best of all ,each subject he talk about he connected to physics by examples and problems

maverick280857

For a great part of the syllabus you could use Advanced Engineering Mathematics by Kreysig (I have the old edition so I have no idea how the new edition looks) for quick introductions and problems. Starting from special functions to group theory, you won't find the material in this book. For that you can also use Arfken/Weber.

cesar314

Ah. I notice that most people have more familiarity with Arfken than with Hassani, and hence tend to propose Arfken. I must say that I have taken a close look at both texts and I prefer Hassani, for the following reason. Arfken may seem more "pedagogical," whatever such a term entails, but there is a sacrifice for completeness. Though it may be late for choosing a text for your course, the subjects you stated are all covered in Hassani, and completely. The examples and problems in Hassani emphasize mathematical skill rather than finagling mathematical methods to suit particular problems. Almost without exception there are concise, clear, and elegant proofs for all the formulas, superior to Arfken. I feel that once you have gained sufficient experience with the algebra and hard analysis, applying the math to physical problems involves less guesswork, instead of wondering about a specific physical example you saw in the book. In particular Hassani has excellent sections on Green's functions (including in several variables), abstract vector spaces, and complex analysis, all of which are very complete and almost eliminate the need for other references.

As to the previous remark on what "mathematical physics" is, the conception that mathematical physics involves only string and quantum field theories is new and at some levels rather mistaken. Traditionally, mathematical physics is the application of rigorous mathematical analysis (in the proper sense) to physical problems of all sorts, and by controlling parameters and limits one discovers properties of the system. Statistical mechanics (including of quantum systems), group theoretical physics (such as particle physics), and relativistic quantum mechanics (including specifically quantum field theories) are all classic examples. For the 'traditional' mathematical physics, look at the voluminous work of Elliott Lieb, who is with Hermann Weyl the paragon of mathematical physicist proper. The modus operandi of the discipline is rather different from string theory and the like, where physical approximations and intuition are still the reigning guide, rather than mathematical rigour. cheers.

ahmedaso8

thanks alot

sinaphysics

i try to term in my uni and final i deduce that sadri is really better but the excercises of orfken is important.