  We investigate a quantum mechanical system on a noncommutative space for
which the structure constant is explicitly time-dependent. Any autonomous
Hamiltonian on such a space acquires a time-dependent form in terms of the
conventional canonical variables. We employ the Lewis-Riesenfeld method of
invariants to construct explicit analytical solutions for the corresponding
time-dependent Schroedinger equation. The eigenfunctions are expressed in terms
of the solutions of variants of the nonlinear Ermakov-Pinney equation and
discussed in detail for various types of background fields. We utilize the
solutions to verify a generalized version of Heisenberg's uncertainty relations
for which the lower bound becomes a time-dependent function of the background
fields. We study the variance for various states including standard Glauber
coherent states with their squeezed versions and Gaussian Klauder coherent
states resembling a quasi-classical behaviour. No type of coherent states
appears to be optimal in general with regard to achieving minimal
uncertainties, as this feature turns out to be background field dependent.
