  We study theoretically two consequences of the mixed classical phase space
for three repulsively-interacting bosonic particles in a circular trap. First,
we show that the energy levels of the corresponding quantum system are well
described by a Berry-Robnik distribution. Second, we identify stationary
quantum states whose density is enhanced along the stable classical periodic
trajectories, and calculate their energies and wavefunctions using the
semiclassical Einstein-Brillouin-Keller (EBK) theory. Our EBK results are in
excellent agreement with our full-fledged finite-element numerics. We discuss
the impact of discrete symmetries, including bosonic exchange symmetry, on
these classically localized states. They are within experimental reach, and
occur in the same range of energies as the quantum scar reported in our
previous work [Phys. Rev. A 107, 022217 (2023)].
