  The notion of the quantum angle is introduced. The quantum angle turns out to
be a metric on the set of physical states of a quantum system. Its kinematics
and dynamics is studied. The certainty principle for quantum systems is
formulated and proved. It turns out that the certainty principle is closely
connected with the Heisenberg uncertainty principle (it presents, in some
sense, an opposite point of view). But at the same time the certainty principle
allows to give rigorous formulations for wider class of problems (it allows to
rigorously interpret and ground the analogous inequalities for the pairs of
quantities like time - energy, angle - angular momentum etc.)
