Talk:Mod:Hunt Research Group/angular schrodinger

The Schrödinger equation for a general system is

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

where $\mu$ is the mass.

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

$V=-\frac{e^2}{4\pi {ϵ}_{0}r}$

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:

$x=r\sin \theta \cos \phi$

$y=r\sin \theta \sin \phi$

$z=r\cos \theta$