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Polar coordinates change

  1. Dec 4, 2005 #1
    how do you change the schrodinger's equation into the spherical polar coordinates?
  2. jcsd
  3. Dec 4, 2005 #2


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    Staff: Mentor

    Look up the chain rule for partial derivatives, and the equations that give you [itex]x, y, z[/itex] in terms of [itex]r, \theta, \phi[/itex] for spherical coordinates. Use these to re-write the derivatives [itex]\partial^2 \psi / \partial x^2[/itex] etc. into the derivatives [itex]\partial^2 \psi / \partial r^2[/itex] etc. There's a lot of algebra. The final result (which you should be able to see in your textbook) contains both first- and second-order derivatives.
    Last edited: Dec 4, 2005
  4. Dec 4, 2005 #3


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    Homework Helper

    The coordinate-free form of the S.E. is:

    [tex]i\hbar\frac{\partial \Psi(\vec r,t)}{\partial t}=-\frac{\hbar^2}{2m}\nabla^2 \Psi(\vec r,t)+V\Psi(\vec r,t)[/tex]

    You can (should) look up the laplacian operator [itex]\nabla^2[/itex] in various coordinate systems in your textbook. There's not much physics to be learned by deriving it.
  5. Dec 5, 2005 #4
    thank you very much! :)
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