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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The Born series expansion

Loading...

Similar Threads for Born series expansion |
---|

A In what sense does MWI fail to predict the Born Rule? |

B Is Max Born's probabilistic proposal artificial? |

Insights A First Idea of Quantum Field Theory - 20 Part Series - Comments |

B Born rule and thermodynamics |

**Physics Forums | Science Articles, Homework Help, Discussion**