  In the studies of the squeezing it is customary to focus more attention on
the particular squeezed states and their evolution than on the dynamical
operations that could squeeze simultaneously some wider families of quantum
states, independently of their initial shape. We look for new steps in this
direction, carried out by softly acting external fields which might produce the
squeezing of the canonical observables $q,p$ of charged particles. The works on
these problems collect so many valuable results that the question is whether
something more is indeed something more in our knowledge. Yet we decided to
present some exactly solvable cases of the problem which appear in the
symmetric evolution intervals permitting to find explicitly the time dependence
of the external fields needed to generate the required evolution operators.
Curiously, our results are interrelated with a simple anti-commuting algebra of
Toeplitz which describes the problem more easily than the frequently used
Ermakov--Milne invariants. Some trending topics, as well as some fundamental
problems in quantum theory, might also be involved.
