Robb and Bonifacio (2011) claimed that a previously neglected quantum effect
results in noticeable changes in the evolution of the energy distribution
associated with spontaneous emission in long undulators. They revisited
theoretical models used to describe the emission of radiation by relativistic
electrons as a continuous diffusive process, and claimed that in the asymptotic
limit for a large number of undulator periods the evolution of the electron
energy distribution occurs as discrete energy groups according to Poisson
distribution. We show that these novel results have no physical sense, because
they are based on a one-dimensional model of spontaneous emission and assume
that electrons are sheets of charge. However, electrons are point-like
particles and, as is well-known, the bandwidth of the angular-integrated
spectrum of undulator radiation is independent of the number of undulator
periods. If we determine the evolution of the energy distribution using a
three-dimensional theory we find the well-known results consistent with a
continuous diffusive process. The additional pedagogical purpose of this paper
is to review how quantum diffusion of electron energy in an undulator with
small undulator parameter can be simply analyzed using the Thomson
cross-section expression, unlike the conventional treatment based on the
expression for the Lienard-Wiechert fields