# Scattering off two centers

1. May 22, 2010

### quZz

Hello to all and each one of you!

I'm a bit confused about solving Shoroedinger equation
$$\nabla^2 \psi + (p^2 - 2mU(\textbf{r})) \psi = 0,$$
for scattering problem
$$\psi(|\textbf{r}|\to \infty) \sim e^{i\textbf{pr}} + f(\theta,\phi) e^{ipr}/r$$
if potential is of the form
$$U(\textbf{r})=V_1(|\textbf{r}|) + V_2(|\textbf{r}-\textbf{a}|).$$

Assuming potentials are not singular and decrease rapidly enough at long distance what is the best choice of coordinates and what are the corresponding initial/boundary conditions for analytical analysis and numerical calculation?

Thanks for any help