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Good Quantum physics book WITH math

  1. Apr 12, 2004 #1
    Hey guys,

    I'm very interested in physics but I am studying computer science at univeristy so I dont get to learn it formally anymore. However, I still read to learn. I recently read Einsteins book on relativity and Stephen Hawking's A Brief History of Time. I now want to read a good book just on quantum physics, however I would like one that contains maths as well. My main annoyance with A Brief History of Time was that there was no maths whatsoever. However, I have found that most books seem to be either completely void of maths or contain very high level maths that I wouldn't be able to understand.

    To let you know what kind of maths level I am at, I took both Maths and Further Maths at A-level and got 2 A's. I'm good with maths, but I dont really get to do too much "normal" maths anymore since I am studying computer science now, so bear in mind there is a limit to my knowledge.

    For you americans that dont know what A-levels are (UK thing), it means that I basically spent 2/3rds of my time at school between 16 and 18 studying maths alone. In terms of pure maths, I know fairly advanced differentiation and integration, reduction formulae, complex numbers, differential equations (1st and 2nd order), hyperbolic functions and all that type of stuff (lots more i can't remember).

    Bearing that in mind, is there a particular book that would be suited to me? I'm currently thinking about getting either Schrodingers kittens or the New Quantum Universe, but from what I have read it seems they contain minimal if any maths, and certainly not any calculus.


  2. jcsd
  3. Apr 12, 2004 #2


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    The thread https://www.physicsforums.com/showthread.php?t=13990 mentions some interesting books, some of them including math. The problem about this it that almost every book expects you learn the math by doing the exercises, and doing them requires a tutor :-(
  4. Apr 12, 2004 #3
  5. Apr 12, 2004 #4
    I find that most physicist here have an indifferent attitude towards Hawking. They said Hawking will mislead you. So I would start with Brian Greene and Richard Feynman.
  6. Apr 13, 2004 #5
    You need to have a basic grounding in differential equations and the physics of waves, including Fourier analysis before you embark on a mainstream quantum physics textbook. Statistics to the level where you know what a mean and a standard deviation is and how to use them is also a good idea, but you might already know this from A level. There are many good books on all these subjects at an undergraduate level. It is also advisable to learn classical mechanics, including the treatment of rotating objects because many concepts are transferred directly across to quantum mechanics. It is a good idea to get up to the Lagrangian and Hamiltonian formulations of classical mechanics, because these are the most directly relevant for QM, but you can probably skip over these for now.

    However, if you do not want to go through all this, then you can learn a lot about the 'weird' aspects of QM from the book "The Meaning of Quantum Theory" by Baggot. This is the part of the subject that a lot of the popular accounts focus on in any case. It is one of the few books about the foundations of quantum mechanics that is written at the undergraduate level. It uses maths where necessary, but it is not too advanced. I believe that Baggot also has a more recent title along similar lines, which is somewhat more up-to-date, but the basics are still the same.
  7. Apr 13, 2004 #6
    Ok thanks a lot guys. I do have a basic grounding in differential equations and the physics of waves but I don't know Fourier analysis (but know of it). I know some stats too (certainly enough to know what mean and standard deviation are anyhow :)), although it generally bores me hehe. I always liked classical mechanics in maths and was good at it so I dont think I have a problem there. I don't know what Langragian or Hamiltonian formulations of it are though but it maybe that I know it and just dont know the names. I'll look it up.

    The book by baggot you mention, slyboy, sounds like my kind of thing. Thanks a lot, i'll check it out.
  8. Apr 13, 2004 #7
    BTW does anyone know much about the New Quantum Universe by Hey and Walters? How about Schrodingers Kittens? Are they any good too? Especially in comparison to The Baggott book that slyboy mentioned.

    In particular, would it be worth reading Schrodingers kittens or the New Quantum Universe before venturing onto the Baggott book? Bearing in mind my current knowledge of quantum physics is mainly only what is contained within A Brief History of Time.

    Thanks again guys,

    Last edited: Apr 13, 2004
  9. Apr 13, 2004 #8


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    The math in Quantum is not that hard, but it is very, very different. That makes it one of the harder things to learn solo, and easier to learn from a teacher.

  10. Apr 13, 2004 #9


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    You will either need to read up on, or else rely on past reading on, linear algebra and vector spaces. The fact that the multiplication of square matrices is, in general, a noncommutative operation is of critical importance in quantum theory, both in its nonrelativistic formulation and relativistic. A course in linear algebra may not discuss Hilbert spaces, but if you already know what a vector space is, it is a short leap to Hilbert spaces, which are just vector spaces with some additional nice properties that make them easy to deal with when representing physical states and operators on those states.
  11. Apr 16, 2004 #10
    Re: New Quantum Universe.

    That is a very good book and I enjoyed it immensely. If you can get hold of it then do.
  12. Apr 16, 2004 #11
    If your math is up to it I would recommend reading Baggot first because it is a much more balanced and accurate account than the other books. In fact, the problem with most books in this area is that they tend to come down in favour of a particular interpretation of quantum mechanics and it can be difficult to separate the scientific facts from the authors own opinion. In Search of Schrodinger's Cat and Schrodinger's Kittens are very good non-technical introductions to the subject, but the emphasis on the many-worlds interpretation is rather unfortunate in my opinion.

    The Lagrangian and Hamiltonian forumulations of classical mechanics are not covered at A level, but they are very elegant and you would enjoy learning about them if you like mechanics and have a mathematical bent. You need a bit of extra maths to understand them (calculus of variations) but this is covered in most university level textbooks on the subject. As I said, this is not essential for a first pass at quantum mechanics, but you will have a better appreciation of how quantum and classical mechanics are related if you learn about them.

    Note that the Lagrangian formulation is only really needed if you intend to go as far as quantum field theory, which you need to do if you want to understand how quantum mechanics fits in with relativity. Ordinary quantum mechanics is usually formulated in a way that is closer to the Hamiltonian version of classical mechanics. However, most textbooks cover Lagrangian mechanics first and then derive Hamiltonian mechanics from it because it is simpler to understand this way round.

    As a first technical QM text I would recommend "Quantum Mechanics" by Rae. It is pretty much the standard text used by most British universities. A lot of people on this board have been talking about Griffith, which is presumably more popular in the States (I have never read it so I cannot comment). For mathematical background, I recommend picking up a copy of "Mathematical methods in the physical sciences" by Boas. It should be adequate to plug any gaps in your mathematics, e.g. Fourier Analysis, and contains more or less everything you need for the first couple of years of a physics degree in the UK.
  13. Apr 17, 2004 #12


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    "Mathematics of classical and quantum physics" by Byron and Fuller probably includes the math you need for studying QM on a basic level. And it's quite cheap too...
  14. Apr 18, 2004 #13
    I have to say that my first pass in quantum mechanics (without Hamiltonian in advanced mechanics) made little sense to me. After studying the hamiltonian for classical mech. it all made much more sense. Besides it was good to know how my professor really did all those tough freshman mechanics problems he tortured us with.

    I can't second this suggestion enough. Such a helpful book for physics & engineering students.
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