  In this paper, we construct integrals of motion in a para-Bose formulation
for a general time-dependent quadratic Hamiltonian, which, in its turn,
commutes with the reflection operator. In this context, we obtain
generalizations for the squeezed vacuum states (SVS) and coherent states (CS)
in terms of the Wigner parameter. Furthermore, we show that there is a
completeness relation for the generalized SVS owing to the Wigner parameter. In
the study of the probability transition, we found that the displacement
parameter acts as a transition parameter by allowing access to odd states,
while the Wigner parameter controls the dispersion of the distribution. We show
that the Wigner parameter is quantized by imposing that the vacuum state has
even parity. We apply the general results to the case of the time-independent
para-Bose oscillator and find that the mean values of the coordinate and
momentum have an oscillatory behavior similarly to the simple harmonic
oscillator, while the standard deviation presents corrections in terms of the
squeeze, displacement, and Wigner parameters.
