  This contribution to the present Workshop Proceedings outlines a general
programme for identifying geometric structures--out of which to possibly
recover quantum dynamics as well--associated to the manifold in Hilbert space
of the quantum states that saturate the Schr\"odinger-Robertson uncertainty
relation associated to a specific set of quantum observables which characterise
a given quantum system and its dynamics. The first step in such an exploration
is addressed herein in the case of the observables Q and P of the Heisenberg
algebra for a single degree of freedom system. The corresponding saturating
states are the well known general squeezed states, whose properties are
reviewed and discussed in detail together with some original results, in
preparation of a study deferred to a separated analysis of their quantum
geometry and of the corresponding path integral representation over such
states.
