Laplacian of 1/sqrt(x^2+y^2+z^2)

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SilverKing

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Dec 25, 2013
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Hi everyone,


Our lecturer asked us the following:

Prove for the following function f=1/sqrt(x^2 + y^2 + z^2) that d2f/dx2 + d2f/dy2 + d2f/dz2 = 0 (The Laplacian Operator)
Click to expand...

I tried so hard to prove it but I got nothing. I asked many people and all of them said that it isn't equal to zero, even Wolfram says so (http://www.wolframalpha.com/input/?i=laplacian+%281%2Fsqrt%28x^2+%2B+y^2+%2B+z^2%29%29%29).

I need a final confirmation: Can this function second derivatives be equal to zero or not?


Thanks in advance.
 
SilverKing said:
Hi everyone,


Our lecturer asked us the following:



I tried so hard to prove it but I got nothing. I asked many people and all of them said that it isn't equal to zero, even Wolfram says so (http://www.wolframalpha.com/input/?i=laplacian+%281%2Fsqrt%28x^2+%2B+y^2+%2B+z^2%29%29%29).

I need a final confirmation: Can this function second derivatives be equal to zero or not?


Thanks in advance.
Click to expand...

Did you calculate δ2f/δx2 , δ2f/δy2 & δ2f/δz2 ?

If you did just add those up - and see!

If you did not - do it now and add those up!

Anyway - you do not need LT for these.
 
It would be:
Untitled.png


And as far as I know, that is not equal to zero.
 
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