  The quantization of the forced harmonic oscillator is studied with the
quantum variable ($x,\hat v$), with the commutation relation $[x,\hat
v]=i\hbar/m$, and using a Shr\"odinger's like equation on these variable, and
associating a linear operator to a constant of motion $K(x,v,t)$ of the
classical system, The comparison with the quantization in the space ($x,p$) is
done with the usual Schr\"odinger's equation for the Hamiltonian $H(x,p,t)$,
and with the commutation relation $[x,\hat p]=i\hbar$. It is found that for the
non resonant case, both forms of quantization brings about the same result.
However, for the resonant case, both forms of quantization are different, and
the probability for the system to be in the exited state for the ($x,\hat v$)
quantization has less oscillations than the ($x,\hat p$) quantization, the
average energy of the system is higher in ($x,\hat p$) quantization than on the
$(x,\hat v$) quantization, and the Boltzmann-Shannon entropy on the ($x,\hat
p$) quantization is higher than on the ($x,\hat v$) quantization.
