  The kinematical foundations of Schwinger's algebra of selective measurements
were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of
this, a new picture of quantum mechanics based on groupoids was proposed. In
this paper, the dynamical aspects of the theory are analysed. For that, the
algebra generated by the observables, as well as the notion of state, are
dicussed, and the structure of the transition functions, that plays an
instrumental role in Schwinger's picture, is elucidated. A Hamiltonian picture
of dynamical evolution emerges naturally, and the formalism offers a simple way
to discuss the quantum-to-classical transition. Some basic examples, the qubit
and the harmonic oscillator, are examined, and the relation with the standard
Dirac-Schr\"odinger and Born-Jordan-Heisenberg pictures is discussed.
