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Scattering off two centers

  1. May 22, 2010 #1
    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
  2. jcsd
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