Page "Quantum electrodynamics" Paragraph 21

Suppose we start with one electron at a certain place and time ( this place and time being given the arbitrary label A ) and a photon at another place and time ( given the label B ).

A typical question from a physical standpoint is: ' What is the probability of finding an electron at C ( another place and a later time ) and a photon at D ( yet another place and time )?'.

The simplest process to achieve this end is for the electron to move from A to C ( an elementary action ) and that the photon moves from B to D ( another elementary action ).

From a knowledge of the probabilities of each of these subprocesses – E ( A to C ) and P ( B to D ) – then we would expect to calculate the probability of both happening by multiplying them, using rule b ) above.

This gives a simple estimated answer to our question.

Compton scattering But there are other ways in which the end result could come about.

The electron might move to a place and time E where it absorbs the photon ; then move on before emitting another photon at F ; then move on to C where it is detected, while the new photon moves on to D. The probability of this complex process can again be calculated by knowing the probabilities of each of the individual actions: three electron actions, two photon actions and two vertexes – one emission and one absorption.

We would expect to find the total probability by multiplying the probabilities of each of the actions, for any chosen positions of E and F. We then, using rule a ) above, have to add up all these probabilities for all the alternatives for E and F. ( This is not elementary in practice, and involves integration.

) But there is another possibility: that is that the electron first moves to G where it emits a photon which goes on to D, while the electron moves on to H, where it absorbs the first photon, before moving on to C. Again we can calculate the probability of these possibilities ( for all points G and H ).

We then have a better estimation for the total probability by adding the probabilities of these two possibilities to our original simple estimate.

Incidentally the name given to this process of a photon interacting with an electron in this way is Compton Scattering.