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Solving Poissons equation with a delta function in RHS using separation of variables.

  1. Sep 14, 2011 #1
    Hi Everyone,

    I am trying to solve the partial differential equation given below:
    [itex]\Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon}[/itex]
    where [itex]f(x,y,z)=1[/itex] at one point and zero elsewhere.
    This is the poisons equation for a point charge inside a conducting box.

    Can this be solved using the variable separable method?

    When I work through it I get:

    [itex]\frac{1}{X(x)}\frac{d^2X(x)}{dx^2}+\frac{1}{Y(y)} \frac{d^2Y(y)}{dy^2}+\frac{1}{Z(z)}\frac{d^2Z(z)}{dz^2}=\frac{qf(x,y,z)}{\epsilon X(x)Y(y)Z(z)}[/itex]

    If this cannot be solved using this method. What others methods can I use. If some one can give me a reference I am thankful.
     
  2. jcsd
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