does anybody know the tranformation from the cartesian to polar coordinates of the laplacian?

Question

i want it analitically

Answer 1

The easiest way is to use the metric, aka chain rule. For example (all d's are "dells" partial der.)

d/dx = (dr/dx)(d/dr) + (d(theta)/dx)(d/d(theta) + (d(phi)/dx)(d/d(phi)

= (dx/dr)^(-1)(d/dr) . . .

= (d(rcos(theta))/dr)^(-1)(d/dr) . . .
= (1/(cos(theta))(d/dr) . . .

Then you can find out what d/dx(d/dx) is . . .

Answer 2

x = rcos(o)
y = rsin(o)
z = z

The results are written in each of the links after the laplacian transform

A mess to show on answers with some equation editor.
Hope that helps.