  The inexactness of the time-dependent Schr\"odinger equation of a charged
particle in an external electromagnetic field is discussed in terms of the
damping effect of the radiation. A possible improvement is to add a nonlinear
term representing this effect to the linear Schr\"odinger equation. Conditions
for the nonlinear term are investigated and it is demonstrated that the
obtained nonlinear Schr\"odinger equation may present state evolutions similar
to the wave-function reduction and transitions between stationary states.
