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Proof involving divergence and gradients

  1. Dec 15, 2011 #1
    del^2([itex]\Phi[/itex]^2)=( 2[itex]\Phi[/itex]del^2)(2||grad[itex]\Phi[/itex]||^2)

    typing out my entire solution will take me ages so I'm going to verbally explain what i've done. I tried to work on the right side of the equation to compress it and make it equal to the left side. it just isnt working. I took the magnitude of the gradient, squared it and plugged that into the equation. Then I plugged the laplacian ino the equation. When I get to the end of the compressing process. I get to this an then I have no idea where to go from here:
    2∂^2[itex]\Phi[/itex]([itex]\Phi[/itex]+1){(1/∂(x^2))+(1/∂(y^2))+(1/∂(z^2))
     
  2. jcsd
  3. Dec 16, 2011 #2
    Sorry can you please use the correct latex codes? It's a pain to read it.

    For the del or grad operator, use \nabla

    for (partial) differentiation, use \frac{ \partial^2 ... }{ \partial x^2}

    or if the expressions substituted in the "..." is long, it's often prettier if one writes \frac{ \partial^2 }{ \partial x^2} \left( ... \right)
     
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