  We present a method for comparing the classical and quantum calculations of
the electric quadrupolar Love number $k_2$ and show that our previous
derivation of the quantum Love number of a quantum blackhole matches exactly
the classical calculation of $k_2$ when quantum expectation values are replaced
by the corresponding classical quantities, as dictated by the Bohr
correspondence principle. The standard derivation of $k_2$ for classical
relativistic stars relies on fixing boundary conditions on the surface of the
star for the Einstein equations in the presence of an external perturbing
field. An alternative method for calculating $k_2$ uses properties of the
spectrum of the non-relativistic fluid modes of the star. We adopt this
alternative method and use it to derive an effective description of the
interior modes in terms of a collection of driven harmonic oscillators
characterized by different frequencies and amplitudes. We compare these two
classical methods and find that most of the interior information can be
integrated out, reducing the problem of calculating $k_2$ to fixing a single
boundary condition for the perturbed Einstein equations on the surface of the
deformed star. We then determine this single boundary condition in terms of the
spectrum of the object and proceed to identify the relationship between
classical quantities and quantum expectation values and to verify the agreement
between the results of the effective classical calculation and the quantum
calculation.
