  Motivated by the recent article of P. Shea {\it et al.} [Am. J. Phys. {\bf
77} (6), 2009] we examine the exactly solvable problem of two harmonically
trapped ultra-cold bosonic atoms interacting {\it via} a short range potential
in one and two dimensions. A straightforward application in one dimension shows
that the energy spectrum is universal, provided that the range of the potential
is much smaller than the oscillator length, in addition to clearly illustrating
why regularization is not required in the limit of zero range. The two
dimensional problem is less trivial, requiring a more careful treatment as
compared to the one dimensional case. Our two dimensional analysis likewise
reveals that the low-energy physics is also universal, in addition to providing
a simple method for obtaining the appropriately regularized two dimensional
pseudopotential.
