Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What kind of differential equations one must know for QM?

  1. Jan 13, 2016 #1
    I will be taking a first course on Quantum Mechanics and just wanted to know what kind of ordinary differential equations must i know before going into the course. Thank you!
     
  2. jcsd
  3. Jan 13, 2016 #2

    Krylov

    User Avatar
    Science Advisor
    Education Advisor

    As far as ODEs are concerned, boundary value problems for second order equations (in particular: Sturm-Liouville problems) come to mind. They often arise when studying systems in QM on a bounded spatial domain and applying a technique called "separation of variables".

    However, my experience from when I was an undergraduate is that most first courses on QM will be quite gentle on the mathematics, introducing unknown mathematical concepts along the way. So there is no need to first read a book on boundary value problems before taking your QM course. If you find the mathematics by itself interesting, you can then choose to read more about it and people here can provide you with references.
     
  4. Jan 13, 2016 #3

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    Probably almost all differential equation problems in QM are encountered in the Schrödinger equation in position basis. The very first one you will most likely encounter in your course is a Helmholtz-type differential equation arising in infinite well problem. Others will be Hermite differential equation, Laguerre differential equation, and associated Legendre differential equation. Anyway, just read through the chapter on differential equation in your textbook, you will hardly miss those needed in QM.
     
    Last edited: Jan 13, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What kind of differential equations one must know for QM?
  1. What are the QM (Replies: 20)

  2. QM in one sentence (Replies: 38)

Loading...