my 1st response to Jims 1st proposed L

Jim, I am looking for a solution to this equation L(1/r) = δ(2)(r) = δ(x)δ(y) r = (x,y) r = where L is some differential operator in 2 dimensions, presumably a linear differential operator. I have thought about your suggestion that perhaps Lf = r ∂r2(rf) so this would say r ∂r2(r[1/r] ) = constant * δ(2)(r) r = (x,y) r = First of all, assuming "constant" has no dimensions, the dimensions of the equation are wrong since they say (length)-1 = (length)-2. Apart from that detail, I agree that for r > 0, the equation is true since 0 = 0, but I am unable to see why this would be true for some arbitrary "test function" φ(r), !Syntax Error, I rdr φ(r) r ∂r2(r[1/r] ) = constant * φ(0) You mentioned doing some limiting procedure, but I don't know how to do that. So I continue to be mystified by this little problem. -Phil __________________________________________________________ Jim modified his suggestion on 1.11.11 to be this: (1/r) ∂r2(r[1/r] ) = δ(r) This has two problems. First, the dimensions are still wrong since we have L-3 = L-1 . I could fix that up by saying ∂r2(r[1/r] ) = δ(r)/r What happens if we integrate this from -ε to ε? !Syntax Error, Idr ∂r2(r[1/r] ) = !Syntax Error, Idr δ(r)/r