  In studies of quantum squeezing, the emphasis is typically placed more on
specific squeezed states and their evolution rather than on the dynamical
operations that could simultaneously squeeze a broader range of quantum states,
regardless of their initial configuration. We explore new developments in this
area, facilitated by gently acting external fields which might induce squeezing
of the canonical observables $q$ and $p$ in charged particles. The extensive
research in this field has yielded many valuable insights, raising the question
of whether there is still room for significant new contributions to our
understanding. Nonetheless, we present some exactly solvable instances of this
problem, observed in symmetric evolution intervals. These intervals allow for
the explicit determination of the temporal dependence of external fields
necessary to generate the required evolution operators. Our findings are linked
with a straightforward application of Toeplitz matrices, offering a more
accessible description of the problem compared to the frequently employed
Ermakov-Milne invariants.
