  In previous works we derived equations for the average momentum of
high-energy electrons experiencing quantum radiation reaction (RR) in strong
electromagnetic plane-wave background fields. In this paper we derive similar
equations for the momentum spectrum. We formulate the equations in terms of the
cumulative function and study the relation between the equations for the
spectrum and the equations for the moments, analyze the structure of the
low-energy expansions, and finally explain how our formulation is essentially
in terms of a ``Green's function'' which allows us to study the dynamics
without choosing a specific initial wave packet (or particle-bunch
distribution).
