  We consider the relations between nonstationary quantum oscillators and their
stationary counterpart in view of their applicability to study particles in
electromagnetic traps. We develop a consistent model of quantum oscillators
with time-dependent frequencies that are subjected to the action of a
time-dependent driving force, and have a time-dependent zero point energy. Our
approach uses the method of point transformations to construct the physical
solutions of the parametric oscillator as mere deformations of the well known
solutions of the stationary oscillator. In this form, the determination of the
quantum integrals of motion is automatically achieved as a natural consequence
of the transformation, without necessity of any ansatz. It yields the mechanism
to construct an orthonormal basis for the nonstationary oscillators, so
arbitrary superpositions of orthogonal states are available to obtain the
corresponding coherent states. We also show that the dynamical algebra of the
parametric oscillator is immediately obtained as a deformation of the algebra
generated by the conventional boson ladder operators. A number of explicit
examples is provided to show the applicability of our approach.
