  The reformulation of Lieb's conjecture, in the frame of the harmonuic
analysis on the SO(3) group, makes it evident that the exact value of the
classical entropy of a pure quantum state, which belongs to the Hilbert space
of a (2J+1)-dimensional, unitary, irreducible representation of the SO(3)
group, depends only on the parameters which characterize the orbits of this
representation. In the case J=1 we give the exact analytic dependence of the
classical entropy of a quantum state on the parameters which characterize the
orbits and as a consequence we obtain a verification of Lieb's entropy
conjecture. We verify this conjecture also for any value of J for the states of
the canonical basis of the Hilbert space of the representation. A natural
generalization of Lieb's entropy conjecture, which is a new "phenomenon" in the
harmonic analysis on SO(3), is discussed in the case J=1.
