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In this article a study was made of the conditions under which a Hamiltonianwhich is an element of the complex $ \left\{ h (1) \oplus h(1) \right\} \uplusu(2) $ Lie algebra admits ladder operators which are also elements of thisalgebra. The algebra eigenstates of the lowering operator constructed in thisway are computed and from them both the energy spectrum and the energyeigenstates of this Hamiltonian are generated in the usual way with the help ofthe corresponding raising operator. Thus, several families of generalizedHamiltonian systems are found, which, under a suitable similaritytransformation, reduce to a basic set of systems, among which we find the 1:1,2:1, 1:2, $su(2)$ and some other non-commensurate and commensurate anisotropic2D quantum oscillator systems. Explicit expressions for the normalizedeigenstates of the Hamiltonian and its associated lowering operator are given,which show the classical structure of two-mode separable and non-separablegeneralized coherent and squeezed states. Finally, based on all the aboveresults, a proposal for new ladder operators for the $p:q$ coprime commensurateanisotropic quantum oscillator is made, which leads us to a class of Chen$SU(2)$ coherent states.

Generalized $ \left\{ h (1) \oplus h(1) \right\} \uplus u(2) $  commensurate anisotropic Hamiltoninan and ladder operators; energy spectrum,  eigenstates and associated coherent and squeezed states