  A Charged harmonic oscillator in a magnetic field, Landau problems, and an
oscillator in a noncommutative space, share the same mathematical structure in
their Hamiltonians. We have considered a two-dimensional anisotropic harmonic
oscillator (AHO) with arbitrarily time-dependent parameters (effective mass and
frequencies), placed in an arbitrarily time-dependent magnetic field. A class
of quadratic invariant operators (in the sense of Lewis and Riesenfeld) have
been constructed. The invariant operators ($\hat{\mathcal{I}}$) have been
reduced to a simplified representative form by a linear canonical
transformation (the group $Sp(4, \mathbb{R})$). An orthonormal basis of the
Hilbert space consisting of the eigenvectors of $\hat{\mathcal{I}}$ is
obtained. In order to obtain the solutions of the time-dependent
Schr\"{o}dinger equation corresponding to the system, both the geometric and
dynamical phase-factors are constructed. Peres-Horodecki Separability Criterion
for the bipartite coherent states corresponding to our system has been
demonstrated.
