  The unusually large "dwarf" galaxy Crater II, with its small velocity
dispersion, $\simeq 3$ km/s, defies expectations that low mass galaxies should
be small and dense. We combine the latest stellar and velocity dispersion
profiles finding Crater II has a prominent dark core of radius $\simeq
0.71^{+0.09}_{-0.08}$ kpc, surrounded by a low density halo, with a transition
visible between the core and the halo. We show that this profile matches the
distinctive core-halo profile predicted by "Wave Dark Matter" as a
Bose-Einstein condensate, $\psi$DM, where the ground state soliton core is
surrounded by a tenuous halo of interfering waves, with a marked density
transition predicted between the core and halo. Similar core-halo structure is
seen in most dwarf spheroidal galaxies (dSph), but with smaller cores, $\simeq
0.25$ kpc and higher velocity dispersions, $\simeq 9$km/s, and we argue here
that Crater II may have been a typical dSph that has lost most of its halo mass
to tidal stripping, so its velocity dispersion is lower by a factor of 3 and
the soliton is wider by a factor of 3, following the inverse scaling required
by the Uncertainty Principle. This tidal solution for Crater II in the context
of $\psi$DM, is supported by its small pericenter of $\simeq 20$ kpc
established by Gaia, implying significant tidal stripping of Crater II by the
Milky Way is expected.
