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We discuss the nature of the low-frequency quadrupole vibrations fromsmall-amplitude to large-amplitude regimes. We consider full five-dimensionalquadrupole dynamics including three-dimensional rotations restoring the brokensymmetries as well as axially symmetric and asymmetric shape fluctuations.Assuming that the time-evolution of the self-consistent mean field isdetermined by five pairs of collective coordinates and collective momenta, wemicroscopically derive the collective Hamiltonian of Bohr and Mottelson, whichdescribes low-frequency quadrupole dynamics. We show that the five-dimensionalcollective Schr\"odinger equation is capable of describing large-amplitudequadrupole shape dynamics seen as shape coexistence/mixing phenomena. Wesummarize the modern concepts of microscopic theory of large-amplitudecollective motion, which is underlying the microscopic derivation of theBohr-Mottelson collective Hamiltonian.

Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics