Re: Re: Re: Divergence and Dirac Delta Function
- To: mathgroup at smc.vnet.net
- Subject: [mg9226] Re: [mg9186] Re: [mg9140] Re: Divergence and Dirac Delta Function
- From: Hugh Walker <hwalker at hypercon.com>
- Date: Fri, 24 Oct 1997 01:00:40 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Elvis Dieguez <elvisum at ibm.net> wrote:
<I understand the theory behind the dirac delta function... however, I
am not clear as to how Mathematica treats the following divergence:
Div[1/r^2]. (Assuming of course that I am using spherical
coordinates--and that 1/r^2 is in the unit r direction). When I
compute that divergence it returns the value -> 0 but I know the
correct value is 4*Pi*DeltaFunction (because of the surface integral!).
Is there anyway of getting this result by computing the above
divergence (and not using the Unit Function). Thanks.>
**********************************
Recall that the relation in question is
Div[{x,y,z}/r^3] = 4 Pi delta[x] delta[y] delta[z] The
RHS is a product of three "1-dimensional" delta functions not to be
confused with delta[r] == delta[Sqrt[x^2+y^2+z^2]]. The present version
of Mathematica has not been trained to remember the above identity.
Perhaps this reminder will help.
Hugh Walker
Gnarly Oaks
Phone: (713) 729-3093