  We consider an isotropic two dimensional harmonic oscillator with arbitrarily
time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily
time-dependent magnetic field $B(t)$. We determine two commuting invariant
observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some
solution of an auxiliary ordinary differential equation and an orthonormal
basis of the Hilbert space consisting of joint eigenvectors $\phi_\lambda$ of
$L,I$. We then determine time-dependent phases $\alpha_\lambda(t)$ such that
the $\psi_\lambda(t)=e^{i\alpha_\lambda}\phi_\lambda$ are solutions of the
time-dependent Schr\"odinger equation and make up an orthonormal basis of the
Hilbert space. These results apply, in particular to a two dimensional Landau
problem with time-dependent $M,B$, which is obtained from the above just by
setting $\Omega(t) \equiv 0$. By a mere redefinition of the parameters, these
results can be applied also to the analogous models on the canonical
non-commutative plane.
