  Dissipation and decoherence, and the evolution from pure to mixed states in
quantum physics are handled through master equations for the density matrix.
Master equations such as the Lindblad equation preserve the trace of this
matrix. Viewing them as first-order time-dependent operator equations for the
elements of the density matrix, a unitary integration procedure can be adapted
to solve for these matrix elements. A simple model for decoherence preserves
the hermiticity of the density matrix. A single, classical Riccati equation is
the only one requiring numerical handling to obtain a full solution of the
quantum evolution. The procedure is general, valid for any number of levels,
but is illustrated here for a three-level system with two driving fields. For
various choices of the initial state, we study the evolution of the system as a
function of the amplitudes, relative frequencies and phases of the driven
fields, and of the strength of the decoherence. The monotonic growth of the
entropy is followed as the system evolves from a pure to a mixed state. An
example is provided by the $n=3$ states of the hydrogen atom in a
time-dependent electric field, such degenerate manifolds affording an
analytical solution.
