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Time-dependent boundary conditions

  1. Mar 25, 2009 #1
    Though this question arose in quantum mechanics, i think it should be posted here.
    Consider a particle in a well with infinite walls:
    [tex]
    $i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$
    [/tex]
    but the wall start to squeeze :devil:
    [tex] $\Psi(x=0,t) \equiv 0$ [/tex]
    [tex] $\Psi(x=a-t,t) = 0$ [/tex]
    In the beginning the state function is known
    [tex] $\Psi(x,t=0) = \varphi(x) [/tex]

    What is the method for solving this type of PDE?
     
  2. jcsd
  3. Mar 26, 2009 #2
    Have you try taking Laplace transform?

    No success? Try another method, separating the variables.
     
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