Hello. I read about the born series in scattering,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

|\psi> = (1+G_0V+\ldots)|\psi_0>

[/tex]

Now when I want to move to spatial representation, the textbook asserts I should get

[tex]

\psi(\vec{r})=\psi_0(\vec{r}) + \int dV' G_0(\vec{r},\vec{r'}) V(\vec{r'})\psi_0(\vec{r'})+\ldots

[/tex]

by operating with [itex]<\vec{r}|[/itex] from the left. However I don't know how to get the 2nd term (the integral). I tried to insert a complete basis like this:

[tex]

<\vec{r}|G_0V|\psi_0> = \int d^3r'<\vec{r}|G_0|\vec{r'}><\vec{r'}|V|\psi_0>

[/tex]

however I don't know how to get [itex]V(\vec{r'})[/itex] from the second bracketed term. Any help?

By the way: is there a "nicer" way to write 'bra' and 'ket' in this forum?

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# The Born series expansion

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