  The model of a two-electron quantum dot, confined to move in a two
dimensional flat space, in the presence of an external harmonic oscillator
potential, is revisited for a specific purpose. Indeed, eigenvalues and
eigenstates of the bound state solutions are obtained for any oscillation
frequency considering both the $1/r$ and $\ln r$ Ans\"atze for inter-electronic
Coulombic-like potentials in 2$D$. Then, it is pointed out that the
significative difference between measurable quantities predicted from these two
potentials can shed some light on the problem of space dimensionality as well
as on the physical nature of the potential itself.
