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Radial component of del^2 in spherical coordinates?

  1. Dec 18, 2008 #1
    I'm doing a question on a 3D isotropic harmonic oscillator. At one point I need to find write the radial component of del^2.

    The lecturer has written 1/r^2 * d/dr * (r^2 * d/dr)

    I don't understand cause it looks like he hasn't actually changed anything, r^2 over r^2 ???
     
  2. jcsd
  3. Dec 18, 2008 #2

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    In Latex, with parenthesis, the expression might be more clear:

    [tex]
    \frac{1}{r^{2}} \frac{d}{dr} \left( r^{2} \frac{d}{dr} \right)
    [/tex]

    You're taking the derivative of r^2*d/dr so the r^2 won't just cancel. Also, del^2 isn't a vector so there aren't components. I guess a more correct way would be the radial term.
     
    Last edited: Dec 18, 2008
  4. Dec 22, 2008 #3
    Ok, I'm really confused.. why isn't the radial part of del^2 in spherical polar coords just dr^2?
     
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