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!

Homework Help: Finding normal coordinates

  1. Jun 19, 2011 #1
    So now it's time for me also to ask a question :)

    1. The problem statement, all variables and given/known data

    I want to calculate a propagator for a coupled (degenerate) system, but somehow it's not possible to find normal coordinates. Maybe they don't exist, could be possible, it's been a time since I did that stuff.

    2. Relevant equations

    C1, C2 are constant, the fields/coordinates are ψ and χ.

    The term in question is C1 ψ ∆ χ + C2 ψ², but it's under an integral sign and integration by parts is permissible. So one could also write - C1 (∇ψ) (∇χ) + C2 ψ², for example.

    3. The attempt at a solution

    The cinetic term decouples in a pretty obvious way by using sum and difference coordinates, but this mixes the mass term.

    I was under the impression that one can always find normal coordinates, but maybe I'm wrong.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted