PHY456H1F: Quantum Mechanics II. Lecture 25 (Taught by Prof J.E. Sipe). Born approximation.
Posted by peeterjoot on December 7, 2011
Peeter’s lecture notes from class. May not be entirely coherent.
READING: section 20 
We’ve been arguing that we can write the stationary equation
Introduce Green function
Suppose that I can find , then
It turns out that finding the Green’s function is not so hard. Note the following, for , we have
(where a zero subscript is used to mark the case). We know this Green’s function from electrostatics, and conclude that
For we can easily show that
This is correct for all because it also gives the right limit as . This argument was first given by Lorentz. We can now write our particular solution
This is of no immediate help since we don’t know and that is embedded in .
Now look at this for
If the scattering is weak we have the Born approximation
Should we wish to make a further approximation, we can take the wave function resulting from application of the Born approximation, and use that a second time. This gives us the “Born again” approximation of
 BR Desai. Quantum mechanics with basic field theory. Cambridge University Press, 2009.