Now consider pair annihilation. In this case we insert for a solution that reduces to at . This positive-energy solution represents an electron that propagates forward in time into the interaction volume, to be scattered backward in time and emerges into a negative energy state. The 'th order amplitude that the electron scatters into a given final state , labelled by the physical quantum numbers , , , is given by
In the language of hole theory this is the 'th order amplitude that a positive-energy electron is scattered into an electron state of negative three-momentum and spin .