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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
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