  Within a scaling ansatz formalism plus Thomas-Fermi approximation, we
investigate the collective excitations of a harmonically trapped boson-fermion
mixture in the collisionless and hydrodynamic limit at low temperature. Both
the monopole and quadrupole modes are considered in the presence of spherical
as well as cylindrically symmetric traps. In the spherical traps, the frequency
of monopole mode coincides in the collisionless and hydrodynamic regime,
suggesting that it might be undamped in all collisional regimes. In contrast,
for the quadrupole mode, the frequency differs largely in these two limits. In
particular, we find that in the hydrodynamic regime the quadrupole oscillations
with equal bosonic and fermionic amplitudes generate an exact eigenstate of the
system, regardless of the boson-fermion interaction. This resembles the Kohn
mode for the dipole excitation. We discuss in some detail the behavior of
monopole and quadrupole modes as a function of boson-fermion coupling at
different boson-boson interaction strength. Analytic solutions valid at weak
and medium fermion-boson coupling are also derived and discussed.
