1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math for QM

  1. Apr 18, 2012 #1
    These are the contents of the books I'm going to be reading to prepare myself for Quantum Mechanics. I was wondering if there any chapters that are not really necessary to learn. For instance, in studying Calculus it seems unlikely to me that infinite series will every be useful, though I might be wrong. I would like to eventually try Particle Physics, Nuclear Physics and Quantum Field Theory and a few basic of String Theory, so if there is some math in these books that is not needed for QM but is needed for the other physics then I should study that too. All this is for my own personal enjoyment and I'm studying it not because I want to be a physicist but because I want to understand the math behind the Big Bang, Cosmology, the Multiverse and the Fine-Tuning Argument.

    Also I realize that more math is needed for physics beyond QM. I'm not worried about that now.

    Screenshot2012-04-10at103604PM.png

    Screenshot2012-04-10at103616PM.png

    Screenshot2012-04-10at103628PM.png

    Screenshot2012-04-18at41831PM.png

    Screenshot2012-04-18at41838PM.png

    Screenshot2012-04-18at41841PM.png

    Screenshot2012-04-18at30607PM.png

    Screenshot2012-04-18at30623PM.png

    Screenshot2012-04-18at30634PM.png
     
  2. jcsd
  3. Apr 18, 2012 #2
    There are too many chapters there that are unnecessary to learn to even list them all. Actually, to some extent, it's a matter of taste or what you want to do with it. I'm not sure the books you are looking at are going to be a very effective way to learn it. Maybe try Susskind's lectures.



    You couldn't be more wrong. Infinite series are so basic, it's not even funny. For example, quantum field theory is all based on perturbation theory, which, in turn, is based on Taylor series.


    I suggest Penrose's book, the Road to Reality. It's a good study plan for that sort of thing. It does talk about a lot of that stuff, but you'll need to read other things to understand it. But, you should realize what you are talking about is basically almost becoming a physicist. If you're entertained by it, by all means, go for it.


    Maybe you should. More math can help to understand things.
     
  4. Apr 18, 2012 #3
    If you're mostly interested in the physics, I recommend reading through a mathematical methods book like Mathematical Methods in the Physical Sciences by Boas. You'll experience a good chunk of the mathematic used in upper level undergraduate physics courses.
     
  5. Apr 18, 2012 #4
    I'm still looking for a good answer to this question. I dont' really want to get a book on math for physicists because I can only read math books if there is a solution manual. Maybe I could get one of those math books for the physical sciences and just look at what subjects are covered then try to find those subjects in the math books.
     
  6. Apr 18, 2012 #5
    That's a very serious limitation. I'm not sure you are going to get very far if you insist on that. I never even pay attention to solutions or whether there are any, so I can't help with that.

    I guess I can say chapters 1-5 of that linear algebra book are what you really need to know.

    4, 5, 9-11 in the second book. I wouldn't do more than that. I'm not sure if I would do the 3rd book at all, but maybe chapters 1-5, there.
     
  7. Apr 18, 2012 #6
    I'm just starting out. Once I get used to reading math books, hopefully the problem will go away. It's the same with any other foreign language. You start out reading the original text and then the translation, eventually you get better and better and you can read it on your own.
     
  8. Apr 19, 2012 #7

    jgens

    User Avatar
    Gold Member

    I know people have varying opinions on solutions manuals, but I would argue that a solutions manual can only hinder your mathematical development. To be frank, if you absolutely need a solutions manual, that is a sign you are not fully understanding the material you're covering; and hence, you're likely not prepared to move forward with your mathematical studies.
     
  9. Apr 19, 2012 #8
    Anything covered in a mathematical methods book or in a lower division calculus or diff eqs class is useful or else why teach it (basically)? There are things that can be skipped and won't kill you, like that section on the fast fourier transform, but topics in those classes are chosen by their utility.

    Power series are, outside of the notion of differentiation and integration, very likely the most important things you learn in calculus. At this point, many functions such as the exponential, are equivalent to their power series in how I think about them because the power series is so incredibly useful.
     
  10. Apr 19, 2012 #9

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Learning math by relying on a solution manual is like bodybuilding by watching someone else lift weights.
     
  11. Apr 19, 2012 #10
    There's surprisingly *little* quantum mechanics around the big bang and cosmology. Except for the very, very early stages, thermodynamics is more important then QM in cosmology, and what QM there is can be "black boxed".
     
  12. Apr 19, 2012 #11
    Well, there's so much hooplah around QM that you can't really ignore. besides, it all also has real fundamental implications on the ultimate stuff of reality. i also want to find out how nature really ticks, i realize that's a cliche but i'm not in an inventive mood right now.
     
  13. Apr 19, 2012 #12
    In what sense? It's extremely useful, particularly early on, to be able to verify your solution to a problem. It's more like bodybuilding, and following each session by reviewing a video tape of your workout routine to verify that you have the correct form.
     
  14. Apr 19, 2012 #13

    jgens

    User Avatar
    Gold Member

    I might agree if most students used solutions manuals this way, but most do not in my experience. Having a solutions manual often discourages students from spending hours and hours on the difficult problems (which is an important part of learning mathematics). And even if they do still struggle on the problems, the solutions manual discourages them from working on verifying independently that they in fact have a valid solution (which is another crucial part of mathematics).

    Students in general aside, the OP mentioned that he cannot make it through math books without a solutions manual. This suggests a lack of understanding of the material. So in the OP's case, it would seem that he is using solutions manuals in a detrimental way.
     
  15. Apr 19, 2012 #14

    jgens

    User Avatar
    Gold Member

    Although this is really beside the point, I think that it is worth mentioning:

    It's important to realize that quantum mechanics--as well as any other theory put forth in physics--is just a model for 'reality'; it is empirically a very good model for phenomenon on the quantum scale, but it is still a model nonetheless. And honestly, I don't think that any sane physicist would tell you that quantum mechanics is a perfect description of the world (even on the quantum scale).
     
  16. Apr 19, 2012 #15
  17. Apr 19, 2012 #16
    Learning math without a teacher or without a SM is like learning french without a dictionary and a grammar. You can't rely on the text because that's written in French too since mathematicians too often assume that the reader has a high level of knowledge. There is no difference between listening to a teacher or reading a SM. You learn the stuff first, then you gradually get to the point where you can do it on your own. It's the same with French, you read the English translations first, then you gradually get to the point where you don't need the translations. I find that I can learn the material three times faster if I have a SM than if I don't.
     
  18. Apr 19, 2012 #17
    You'd be surprised how much of a weightlifters training is watching and analyzing the technique of other lifters on video.
     
  19. Apr 19, 2012 #18

    jgens

    User Avatar
    Gold Member

    I disagree wholeheartedly here. The way I learned math (starting at the level of calculus) was by sitting down with a book and by working through all of the theorems and exercises without solutions manuals. So it certainly is possible to learn math this way.

    In any case, I know my experience with learning math this way isn't unique either; all of the best math students I know started learning this way from a young age.

    This is a sign that you lack the mathematical maturity for the particular text.

    Again, I disagree wholeheartedly. Listening to a teacher is akin to reading the proofs of whatever theorems are presented in the text. Reading a solutions manual is like asking the smart kid in your class for the answers to your homework problems.

    Your goal should be to really learn the material, rather than to cover the greatest amount of material you can in a short period of time. Really learning and understanding mathematics comes from practice and many hours spent taking wrong turns. That is how you develop an intuition and how you learn to attack the more challenging problems.
     
  20. Apr 19, 2012 #19

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Certainly, you can learn it faster. But is your learning effective??
    The best way to learn is by trying things yourself without help. Only checking the final answer should be allowed. And perhaps letting somebody else (on this forum for example) check out the form once in a while.
    But one should be able to do things without solution manual. It only hinders your learning.
     
  21. Apr 19, 2012 #20

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    You need to decide what your objective is. Do you want to get a good grade, assuming the test questions will be pretty much the same as the questions in the book, or do you want to learn the subject?

    I'm not moralizing about this - it's your choice. The solution manual is a very good tool for the first objective, but a very bad one for the second IMO.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook