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### Topic: eigenfunction  (Read 5864 times)

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#### zeshkani

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##### eigenfunction
« on: February 28, 2008, 08:40:34 PM »
Find the result of operating ∇2 on ( x2 + y2 + z2 ). Is ( x2 + y2 + z2 ) an eigenfunction of ∇2 ? Try
the same problem in polar coordinates; the answer should be the same.

iam totally lost on this question, dont even know were to start

#### Yggdrasil

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##### Re: eigenfunction
« Reply #1 on: February 28, 2008, 08:45:15 PM »
Do you know what the ∇2 operator is?  If not, a good starting point will be the following wikipedia article, especially the section about the Laplacian in three-dimensions:

http://en.wikipedia.org/wiki/Laplacian
http://en.wikipedia.org/wiki/Laplacian#Three_dimensions

#### FeLiXe

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##### Re: eigenfunction
« Reply #2 on: March 02, 2008, 02:45:30 PM »
just do the derivations and summations in cartesian coordinates
then change x^2+y^2+z^2 to polar coordinates and apply the Laplace from wikipedia
Math and alcohol don't mix, so... please, don't drink and derive!

#### Martingale

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##### Re: eigenfunction
« Reply #3 on: March 02, 2008, 10:18:48 PM »
Find the result of operating ∇2 on ( x2 + y2 + z2 ). Is ( x2 + y2 + z2 ) an eigenfunction of ∇2 ? Try
the same problem in polar coordinates; the answer should be the same.

...

Isn't polar coordinates a two-dimensional coordinate system?
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#### FeLiXe

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##### Re: eigenfunction
« Reply #4 on: March 03, 2008, 08:41:30 AM »
in this case they are certainly talking about 3-dimensional spherical polar coordinates
the definition is for example here: http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
Math and alcohol don't mix, so... please, don't drink and derive!