Two complementary methods to describe the collective motion, RPA and Wigner
function moments method, are compared on an example of a simple model -
harmonic oscillator with quadrupole-quadrupole residual interaction. It is
shown that they give identical formulae for eigenfrequencies and transition
probabilities of all collective excitations of the model including the scissors
mode, which here is the subject of our special attention. The exact relation
between the variables of the two methods and the respective dynamical equations
is established. The normalization factor of the "synthetic" scissors state and
its overlap with physical states are calculated analytically. The orthogonality
of the spurious state to all physical states is proved rigorously.Comment: 39 page