  Several authors have used the Heisenberg picture to show that the atomic
transitions, the stability of the ground state and the position-momentum
commutation relation [x,p]=ih, can only be explained by introducing radiation
reaction and vacuum electromagnetic fluctuation forces. Here we consider the
simple case of a nonrelativistic charged harmonic oscillator, in one dimension,
to investigate how to take into account the radiation reaction and vacuum
fluctuation forces within the Schrodinger picture. We consider the effects of
both classical zero-point and thermal electromagnetic vacuum fields. We show
that the zero-point electromagnetic fluctuations are dynamically related to the
momentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the
introduction of the zero-point electromagnetic fields in the vector potential
A_x(t) used in the Schrodinger equation, generates ``double counting'', as was
shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We
explain, in details, how to avoid the ``double counting'' by introducing only
the radiation reaction and the thermal electromagnetic fields into the
Schrodinger equation.
