  We consider the spectrum of two ultracold harmonically trapped atoms
interacting via short-range interactions. The Green's function approach is used
to unify the two and three dimensional cases. We derive criteria for the
universality of the spectrum, i.e. its independence of the details of the
short-range interaction. The results in three dimensions are examplified for
narrow s-wave Feshbach resonances and we show how effective range corrections
can modify the rearrangement of the level structure. However, this requires
extremely narrow resonances or very tight traps that are not currently
experimentally available. In the two-dimensional case we discuss the p-wave
channel in detail and demonstrate how the non-universality of the spectrum
arises within the Green's function approach. We then show that the spectrum is
not particularly sensitive to the short-distance details in the case when the
two-body interaction has a bound state.
