$x=r\cos\theta$, $y = r\sin\theta$
$\theta = \arctan \frac{y}{x}$, $r=\sqrt{x^2 + y^2}$

the laplacian is $\nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2f}{\partial y^2}$