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.