Abstract
Two complementary methods to describe the collective motion, the RPA and the method of Wigner function moments, are compared using a simple model as an example—a harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulas for eigenfrequencies and transition probabilities of all collective excitations of the model, including the scissors mode, which is a subject of our special attention. 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.
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