the harmonic oscillator problem in quantum mechanics is to find operators $a$ and $b$ acting on a hilbert space satisfying the relation $ab-ba=1$. this is one of the physical motivations behind studying the weylalgebra and the enveloping algebra of the heisenberg lie algebra. in this talk, i will present a two-parameter version of this problem and discuss some of the subtleties in looking for simple, primitive factor rings in quantum enveloping algebras.