  Here, the Morgan type uncertainty principle and unique continuation
properties of abstract Schredinger equations with time dependent potentials are
obtained in Hilbert space valued function classes. The equations include linear
operator in abstract Hilbert spaces H dependent on space variables. So, by
selecting appropriate spaces H and operators, we derive unique continuation
properties for numerous classes of Schr\"odinger type equations and its
systems, which occur in a wide variety of physical systems.
