Talk:Mod:Hunt Research Group/angular schrodinger

The Schrödinger equation for a general system is

$-\frac{\hbar^2}{2\mu}\nabla^2\Psi - V\Psi = E\Psi$

where $\mu$ is the mass.

For a hydrogen atom, the potential energy $V$ is

$V = -\frac{e^2}{4 \pi \epsilon_0 r}$

i.e. $V$ is a function of the radial distance $r$ only: $V = V(r)$

By performing a co-ordinate transformation from Cartesian to spherical polars:

$x = r\,\sin\theta\,\cos\varphi$

$y = r\,\sin\theta\,\sin\varphi$

$z = r\,\cos\theta$