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Chaotic quantum billiards on a torus.

  1. Aug 8, 2011 #1

    MathematicalPhysicist

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    Hi, I want to do a similar statistics analysis as in the next paper:
    http://www.phy.bris.ac.uk/people/Berry_mv/the_papers/Berry340.pdf

    But the boundary conditions are on a two dimensioanl torus, so a solution will be of the form
    [tex]u(R)=\sum_{j=1}^{\infty} \sum_{m,n=0}^{\infty} (A_{mn} sin(mXcos(\theta_j)+nYsin(\theta_j)+\phi_j) + B_{mn} cos(mXcos(\theta_j)+nYsin(\theta_j)+\phi_j)[/tex] (have I got it right?!) the problem arises when I impose on it a Dirchlet boundary condition (for example), cause I need f to satisfy: [tex]u(x,0)=u(x,2\pi)=0[/tex] and [tex] u(0,y)=u(2\pi,y)=0[/tex]

    Which doesn't look like something I can solve easily, can I?

    Any help?

    Thanks.
     
    Last edited: Aug 8, 2011
  2. jcsd
  3. Aug 11, 2011 #2
    Surely there are familiar Fourier series tricks you can use with that summation expression...
     
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