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PDE of a function of two variables (cylindrical coordinates with azimuthal symmetry)

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve in cylindrical coordinates
    [itex]-m\delta(z)\delta(\rho-a)=\partial^2_z A(z,\rho)+\partial^2_\rho A(z,\rho)+\frac{1}{\rho}\partial_\rho A(z,\rho)-\frac{1}{\rho^2}A(z,\rho)[/itex]

    Where [itex]\partial_i[/itex] is the partial derivative with respect to [itex]i[/itex].

    2. Relevant equations
    It is suggested to use an integral representation for a delta function (only for the [itex]\rho[/itex] delta), which I think is:
    [itex]\delta(\rho-a)=\frac{1}{2 \pi}\int_{-\infty}^{\infty}e^{i k (\rho-a)}\,\mathrm{d}k[/itex]

    But it could refer to a representation using bessel functions, because I expect there to be bessel functions in the answer.

    3. The attempt at a solution
    My first attempt went with assuming that because there is delta functions, I can initially set those equal to zero and use the separation of variables, and expect the final answer to be in the form of whatever I get. Turns out that doesn't quite work.

    Now I'm a bit lost, anyone have a direction to point me in?
  2. jcsd
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