- #1
LagrangeEuler
- 711
- 22
Laplacian in cylindrical coordinates is defined by
\Delta=\frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial}{\partial \rho}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \varphi^2}+\frac{\partial^2}{\partial z^2}
I am confused. I I have spherical symmetric function f(r) then
\Delta f(r)=\frac{d^2}{dr^2}f(r)+\frac{2}{r}\frac{d}{dr}f(r)
If I worked on function ##f(r)## with Laplacian in cylindrical coordinates. I suppose that f(r)=f(\rho) but then factor ##2## is problem.
\Delta=\frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial}{\partial \rho}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \varphi^2}+\frac{\partial^2}{\partial z^2}
I am confused. I I have spherical symmetric function f(r) then
\Delta f(r)=\frac{d^2}{dr^2}f(r)+\frac{2}{r}\frac{d}{dr}f(r)
If I worked on function ##f(r)## with Laplacian in cylindrical coordinates. I suppose that f(r)=f(\rho) but then factor ##2## is problem.