Talk:Mod:Hunt Research Group/angular schrodinger

The Schrödinger equation for a general system is

<math>-\frac{\hbar^2}{2\mu}\nabla^2\Psi - V\Psi = E\Psi</math>

where <math>\mu</math> is the mass.

For a hydrogen atom, the potential energy <math>V</math> is

<math>V = -\frac{e^2}{4 \pi \epsilon_0 r}</math>

i.e. <math>V</math> is a function of the radial distance <math>r</math> only: <math>V = V(r)</math>

File:Spherical polars.png

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

<math>x = r\,\sin\theta\,\cos\varphi</math>

<math>y = r\,\sin\theta\,\sin\varphi</math>

<math>z = r\,\cos\theta</math>