With the help of some commutators,

The commutator
(with no dot products) can be very useful in calculations.
When the two vectors are multiplied directly, we get something with two Cartesian indices.

The commutator of the vectors is times the identity. This can be used to cast the first term above into something like the other two.

Now we need to put the states in using an identity, then use the commutator with to change to .

(Reminder: is just a number. is a matrix element between states.)

We may now **combine the terms** for elastic scattering.

This is a

Jim Branson 2013-04-22