On effects of K-mixing in wobbling motion

Bohr and Mottelson showed that a quantum rotor with triaxiality shows wobbling motion at high spin under the classical condition, $I \simeq I_1$. Quantum mechanically, we need to reconsider this condition as $I \simeq \langle\hat{I}_1\rangle$ because the Hamiltonian does not commute with $I_1$. In other words, when we call eigenvalues of the angular momentum operator $I_1$ $K$-quantum numbers, $K$ is not a good quantum number in this model. We discuss several effects of $K$-mixing in the wobbling model, and present an view about how the wobbling motion should be understood quantum mechanically.