  In this article the time evolution operator of two interacting quantum
oscillators, whose Hamiltonian is an element of the complex $\left\{ h(1)
\oplus h(1) \right\} \uplus u(2)$ algebra, is analyzed using the Feynman time
ordering operator techniques. This method is consistently used to generate the
conditions and to formally find explicit disentangled expressions for such
operator. In this way, it is shown that all the problem reduces to solve a
complex Riccati-type differential equation. Some closed solutions to this
differential equation are found and then concrete disentangling expressions for
the time-ordered evolution operator are given. Finally, the time evolution of
the coherent states linked to the isotropic 2D quantum oscillator are analyzed
under alternative time-independent an time-dependent Hamiltonian systems.
