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What is the general method for solving Schroedinger equation

[tex]

\nabla^2 \psi(\textbf{r}) + (p^2 - 2mU(\textbf{r}))\psi(\textbf{r}) = 0,

[/tex]

with arbitrary potential [itex]U(\textbf{r})[/itex] that is not singular and decreases rapidly at infinity.

I'm interested in scattering problem, so

[tex]

\psi(\textbf{r}) \sim e^{i\textbf{p}\textbf{r}} + f(p,\textbf{r}/r)\frac{e^{ipr}}{r}

[/tex]

as [itex]r\to\infty[/itex].

What are the corresponding boundary/initial conditions?

Thanks in advance.

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# General method for solving SE

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