  We show that it is possible to associate univocally with each given solution
of the time-dependent Schroedinger equation a particular phase flow ("quantum
flow") of a non-autonomous dynamical system. This fact allows us to introduce a
definition of chaos in quantum dynamics (quantum chaos), which is based on the
classical theory of chaos in dynamical systems. In such a way we can introduce
quantities which may be appelled "Quantum Lyapunov Exponents". Our approach
applies to a non-relativistic quantum-mechanical system of n charged particles;
in the present work numerical calculations are performed only for the hydrogen
atom. In the computation of the trajectories we first neglect the spin
contribution to chaos, then we consider the spin effects in quantum chaos. We
show how the quantum Lyapunov exponents can be evaluated and give several
numerical results which describe some properties found in the present approach.
Although the system is very simple and the classical counterpart is regular,
the most non-stationary solutions of the corresponding Schroeodinger equation
are "chaotic" according to our definition.
