Constrained Evolution in Hilbert Space and Requantization

Constrained dynamics on finite-dimensional trial manifolds of quantum state vectors appears in time-dependent variational calculations. This work presents a requantization method, by which properties of the exact eigenstates can be retrieved from the phase portrait of such approximations. Applications to the coherent states dynamics, small amplitude vibrations and collective rotations, show that this approach extends standard procedures of the quantum many-body theory, such as the method of the projection operators and the random phase approximation.