  Cold Dark Matter (CDM) models struggle to match the observations at galactic
scales. The tension can be reduced either by dramatic baryonic feedback effects
or by modifying the particle physics of CDM. Here, we consider an ultra-light
scalar field DM particle manifesting a wave nature below a DM particle
mass-dependent Jeans scale. For DM mass $m\sim10^{-22}{\rm eV}$, this scenario
delays galaxy formation and avoids cusps in the center of the dark matter
haloes. We use new measurements of half-light mass in ultra-faint dwarf
galaxies Draco II and Triangulum II to estimate the mass of the DM particle in
this model. We find that if the stellar populations are within the core of the
density profile then the data are in agreement with a wave dark matter model
having a DM particle with $m\sim 3.7-5.6\times 10^{-22}{\rm eV}$. The presence
of this extremely light particle will contribute to the formation of a central
solitonic core replacing the cusp of a Navarro-Frenk-White profile and bringing
predictions closer to observations of cored central density in dwarf galaxies.
