  We investigate the charmonium and bottomonium production in $pp$ collisions
using the Wigner densities formalism. The Wigner density of the quarkonia is
approximated by analytical 3-D isotropic harmonic oscillator Wigner densities
with the same root-mean-square radius given by the solution of the
Schr\"odinger equation. This approach reproduces quite well the available
experimental transverse momentum and rapidity distributions.
