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I need advice on upcoming course schedule

  1. Aug 12, 2015 #1
    So I really have a few questions. First, is it wise to take the following classes in the same semester?

    Quantum Mechanics I - At the level of Griffiths' Intro to Quantum Mechanics, chapters 1-5ish

    Classical Dynamics - At the level of Thorton and Marion, Chapters 1-12, ends with coupled oscillations

    Linear Algebra and Matrix Theory - At the level of Andrilli and Hecker. This class is aimed at math
    majors with some emphasis on proofs, chapters 1-5.5, ends with isomorphism and diagonalization of linear operators
    Complex Analysis - At the level of Marsden and Hoffman, Chapters 1-5, ends with conformal mappings

    American Literature - Not very relevant to this discussion

    No that it matters, but I'll be taking 15 hours and I'm a math/physics major at UT Austin.

    You may have noticed that three of these classes is, some might say, essential to learning quantum mechanics. This leads to my second quesion: Would it be better to hold off quantum mechanics for the spring semester and get Classical, Linear Algebra, and Complex Analysis done first? I feel like I might not appreciate quantum mechanics as much, nor be fully capable of understanding or working out the problems if I don't know some of the math and physics. I hear some speak about hamoltonians showing up in Quantum, and I won't get to know about it until much later in my classical dynamics class. What topics from classical dynamics, complex analysis, and Linear Algebra show up in Quantum? Could it possibly be to my advantage to take all the same time that way I learn it and apply it nearly at the the time, hopefully?

    I should perhaps mention that I have elementary knowledge in linear algebra (as far as matrix multiplication) and I only know about complex numbers (no kind of differentiation or integration) with little knowledge of infinite series of complex numbers. Furthermore, the only knowledge I know about classical dynamics is calculus of variations and that's about it other than Newtonian mechanics.

    Thank you.
     
  2. jcsd
  3. Aug 12, 2015 #2
    I would. That way you can concentrate on the physics and not be too distracted by the math. One question what is your background in diff. eq's?
     
  4. Aug 12, 2015 #3
    Yes, I've taken differential equations 1st,2nd ODE's, power solutions, and a little bit of PDEs, particularly the heat equation and Laplace equations
     
  5. Aug 12, 2015 #4
    Regarding PDE special functions plays a big role in QM so familiarity with these is important. have you had any exposure?
     
  6. Aug 12, 2015 #5
    Like which ones are you referring to? I'm familiar with 3-dimensional Dirac delta function or the integral of it,rather. I'm also very familiar with vector calculus. I'm not sure if I remember any other special functions.
     
  7. Aug 12, 2015 #6
    Hermite, Legendre and Bessel functions which are solutions to particular types of diff eq's.
     
  8. Aug 12, 2015 #7
    Just to make sure I assume you have had intermediate E/M.
     
  9. Aug 12, 2015 #8
    No, not hermite, barely touched on Bessel and Legendre functions like once or twice like what seems a long time ago. Yes, I took took E/M at the level of griffiths electrodynamics. I read all of part 1 and the only thing I read from the second was on gauges.
     
  10. Aug 12, 2015 #9
    Great with Griffiths. Familiarity with special functions is an advantage in solving problems in QM.
     
  11. Aug 13, 2015 #10
    So just to be clear, after all that I've told you about my math and physics background, you would recommend I hold off Quantum Mechanics?
     
  12. Aug 13, 2015 #11

    radium

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    What year are you and what other physics classes have you taken so far?
     
  13. Aug 14, 2015 #12
    In terms of courses I've taken, I suppose I'll be Junior, or sophomore, or in between? I've taken modern physics, waves and oscillations which touched on optics +lab, freshman mechanics+lab, freshman E/M +lab. Cal I,II,II, Diff Eqs, Electrodynamics I. I spent two years at another university where I only took math and core classes, no physics, before transferring to UT. I've effectively been in school for 4 years now, and I suspect I might take two more if I want to get two degrees. The reason is I might not make it into a good grad school so might as well get two degrees from a good school and join the work force then try grad school after that. Thanks for taking the time to respond btw, I appreciate it.

    Edit: reason I'm doing two degrees is because I love those two subjects. I find them aesthetically pleasing to my mind, and not mention I love how complex problems (in any field if I find it interesting) can become more accessible to solve if I know more math.
     
    Last edited: Aug 14, 2015
  14. Aug 14, 2015 #13
    You don't really need a full blown complex analysis/variables course for introductory QM unless the lecturer is REALLY gung-ho on maths (e.g. from the Russian school). Just being comfortable with complex numbers generally is probably sufficient. Proper linear algebra on the other hand is probably quite useful as prior knowledge however, even if it's not taught explicitly from a formal point of view, the concepts were quite helpful I found.

    With regards to Hamiltonians, the advice I've been given, and as I encountered them, was that for lower level QM it's generally fine to treat it as a black box of sorts, and just know the Hamiltonian takes a specific form for whatever problems you get, and then as you go into the higher echelons a better understanding of the fundamental maths is more helpful. Again, it depends somewhat on the rigour and style of the course, whether it's more physical intuition based or mathematically based.
     
  15. Aug 15, 2015 #14

    radium

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    Based on the core curriculum I had in undergrad, the logical next step would be to take quantum. I learned most of the relevant math I know from physics classes. I took a graduate mathematical methods of physics course and that gave me the foundation to learn more advanced math for my research.
     
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