  We calculate the propagator and the transition probabilities for a coherently
driven three-state quantum system. The energies of the three states change
linearly in time, whereas the interactions between them are pulse-shaped. We
derive a highly accurate analytic approximation by assuming independent
pairwise Landau-Zener transitions occurring instantly at the relevant avoided
crossings, and adiabatic evolution elsewhere. Quantum interferences are
identified, which occur due to different possible evolution paths in Hilbert
space between an initial and a final state. A detailed comparison with
numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy
of the analytic approximation. We use the analytic results to derive estimates
for the half-width of the excitation profile, and for the parameters required
for creation of a maximally coherent superposition of the three states. These
results are of potential interest in ladder climbing in alkali atoms by chirped
laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a
J=1 level in a magnetic field, and in control of entanglement of a pair of
spin-1/2 particles. The results for the three-state system can be generalized,
without essential difficulties, to higher dimensions.
