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A Laplacian cylindrical coordinates

  1. Dec 8, 2016 #1
    Laplacian in cylindrical coordinates is defined by

    [tex]\Delta=\frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial}{\partial \rho}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \varphi^2}+\frac{\partial^2}{\partial z^2} [/tex]
    I am confused. I I have spherical symmetric function f(r) then
    [tex]\Delta f(r)=\frac{d^2}{dr^2}f(r)+\frac{2}{r}\frac{d}{dr}f(r)[/tex]
    If I worked on function ##f(r)## with Laplacian in cylindrical coordinates. I suppose that [tex]f(r)=f(\rho)[/tex] but then factor ##2## is problem.
     
  2. jcsd
  3. Dec 8, 2016 #2
    I think it is ##f(r)=f(\sqrt{\rho^2+z^2})##.
     
  4. Dec 10, 2016 #3
    Of course. Thanks.
     
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