  We make use of numerical exact diagonalization calculations to explore the
physics of $\nu = 1/2$ bosonic fractional quantum Hall (FQH) droplets in the
presence of experimentally realistic cylindrically symmetric hard-wall
potentials. This kind of confinement is found to produce very different
many-body spectra compared to a harmonic trap or the so-called extremely steep
limit. For a relatively weak confinement, the degeneracies are lifted and the
low-lying excited states organize themselves in energy branches that can be
explained in terms of their Jack polynomial representation. For a strong
confinement, a strong spatial deformation of the droplet is found, with an
unexpected depletion of its central density.
