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

  1. Jun 21, 2006 #1


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    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?
  2. jcsd
  3. Jun 21, 2006 #2


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    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.
  4. Jun 21, 2006 #3
    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.
  5. Jun 21, 2006 #4


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    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?
  6. Jun 21, 2006 #5

    George Jones

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

    For what do you want your choice to prepare you?
  7. Jun 21, 2006 #6


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    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?
  8. Jun 21, 2006 #7

    George Jones

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    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 https://www.physicsforums.com/showpost.php?p=1008436&postcount=60". This may just be extraneous stuff for you. Also, I am unfamiliar with just how good Hassani's style of presentation is.
    Last edited by a moderator: Apr 22, 2017
  9. Jun 22, 2006 #8


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    what topics would you consider as modern mathematical physics?
  10. Jun 22, 2006 #9

    matt grime

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    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.
  11. Jun 23, 2006 #10
    Arfken is the best of all ,each subject he talk about he connected to physics by examples and problems
  12. Jun 27, 2006 #11
    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.
  13. Mar 4, 2007 #12
    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.
    Last edited: Mar 4, 2007
  14. Mar 8, 2007 #13
    thanks alot
  15. Jul 8, 2009 #14
    i try to term in my uni and final i deduce that sadri is really better but the excercises of orfken is important.
  16. Oct 23, 2011 #15
    its really bad there is no solution manual for the exercises which make arfken useless for self study
  17. Oct 25, 2011 #16
    For the most complete book of analysis/mathematical physics, check out “A Course of Modern Analysis” by E. T. Whitaker and G. N. Watson first published in 1902. It was a standard reference for giants such as G. H. Hardy, the great mathematician who brought the world the number theory works of Ramanujan, an enigmatic genius so ahead of his time that mathematicians are still pouring over his notebooks to date. See “Number Theory in the Spirit of Ramanujan” by Bruce C. Berndt, American Mathematical Society, 1996. You’ll need a good background in complex variables to pursue Ramanujan. As for Whitaker and Watson, their book was reprinted (more like poorly photocopied) by Cambridge Press in November of 2009. Allow me to quote an anonymous Amazon.com reviewer. “It is certainly the most useful book of mathematics I ever put my hands on. If you read its page of contents, you'll call it prophetic! Every kind of function he studied became important in theoretical physics some time. The citations go back half 500 years.

    I review more math/physics books througout:


  18. Oct 25, 2011 #17
    The Baierlein text is a fantastic undergraduate introduction into classical mechanics, including mechanics formulated in variational calculus. If you want to understand quantum mechanics, read the graduate text “Classical Mechanics” 3rd ed. by Herbert Goldstein, Addison Wesley, 2001. I love my 2nd ed. The 3rd ed. better reflects the use of computers and nonlinearities in mechanics. First edition dates back to 1950.

    Two books I wished I would have read around the time I took undergrad mechanics are:

    a. Calculus of Variations, L. D. Elsgolc, Dover Publications. Originally written in Russian, this book was first published in English in 1961. Using clear notation, Elsgolc develops the calculus of variations side-by-side with ordinary differential calculus. Starting with a challenge to Isaac Newton, this calculus originated from extremization problems in physics, e.g., least time, maximum entropy, least action. The Standard Model, general relativity, string theories, to name but a few, are expressible in terms of least action. Ideally this book should be read before graduate work in physics, probably concurrently with junior level mechanics.
    b. Variational Principles in Dynamics and Quantum Theory, W. Yourgrau and S. Mandelstam, Dover Publications. Tracing the evolution of the concept of the innate economy of nature (least action) from the Greeks through to Fermat’s principle of least time and Maupertuis’ le principe de la moindre quantité d’action (least action) in 1744, this book traces the development of the equations of Lagrange, Hamilton, Hamilton-Jacobi, etc., in classical mechanics and electrodynamics to the various historical paths to quantum physics including those of Feynman and Schwinger. This book should probably be read concurrently during the first year of graduate school, if not at the completion of the undergraduate degree. Without these readings, or similar, the use of the principle of least action is little more than a physics gimmick.

    I review texts/literature/key physics ideas/key math methods from junior level physics to graduate/postgraduate levels. See: https://www.physicsforums.com/showthread.php?t=540829

    Hope this helps,

    Alex A.
  19. Oct 26, 2011 #18


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    I really like Whitaker and Watson too, although I don't think it would be a very good text for a class. In any case it can be had (legally) for free at:

    Arfken or Hassani are both better for a course, I would think. Another option from yesteryear is Matthews and Walker.

    Last edited: Oct 26, 2011
  20. Nov 14, 2011 #19
    I think it is THE pity that somebody cant get vital information for his EDUCATION!!!!

    The succsess of USSR in 20th centure was partly defined by our's laws in rejecting author ability to reject people accessing to vital information while somebody is educating.
  21. Feb 6, 2012 #20
    I know this is an old thread, but I have all three of the books in question.

    Boas: Undergraduate. Cookbook. "For this problem category, turn this crank." Check out Riley, Hobson & Bence's book.

    Arfken: Graduate. Not even a cookbook. Everyone says "get Arfken." I didn't see any effort at pedagogy exerted in this one. It's a collection of homework problems.

    Hassani: Graduate. A blueprint of how mathematics and physics really join together. This is how you get to be a pro. The author gave a damn.

    Some bloodied physics grad mentioned Matthews & Walker. It's deliberately obscure in its presentation. (Says so in the preface). Waste of trees.

    Anyhow, my opinions.
    Last edited: Feb 6, 2012
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