Strange Laplacian of 1/|x-x’| ?

[abcdefg10645]

Strange Laplacian of 1/|x-x’| !?

Please read the file first (http://www.pa.msu.edu/courses/2007fall/PHY481/lectures/lecture08.pdf" ) ..


and look into page 8

there is a sentence like this "Evaluate right side with sphere, radius R around origin"

Now there comes up against a question :

Why do we have to use "sphere around origin" (← That is often used in physic. But I need a general elucidate...)

how about any surface around the origin?

 

[Hootenanny]

Of course Gauss' theorem is valid for any closed surface, however, one chooses the surface to simplify the process of integration. Since the Laplacian is spherically symmetric, it makes sense to use a spherical surface. Obviously other problems will have other symmetries and you should choose your surface appropriately.

 

[abcdefg10645]

Of course Gauss' theorem is valid for any closed surface, however, one chooses the surface of integration to simplify the process of integration. Since the Laplacian is spherically symmetric, it makes sense to use a spherical surface. Obviously other problems will have other symmetries and you should choose your surface appropriately.

Umm,thank you!

I need to go to bed now (because the zone here is diffirent from yours >< (Taiwan))

although I want to learn more things from you...


THX again!

 

[samalkhaiat]

Please read the file first (http://www.pa.msu.edu/courses/2007fall/PHY481/lectures/lecture08.pdf" ) ..


and look into page 8

there is a sentence like this "Evaluate right side with sphere, radius R around origin"

Now there comes up against a question :

Why do we have to use "sphere around origin" (← That is often used in physic. But I need a general elucidate...)

how about any surface around the origin?

We use sphere so that the resulting surface integral can be done.

See post #10 in

www.physicsforums.com/showthread.php?t=200580


regards

sam