A quantum propagation method in D-dimensional problem (D = 1, 3,5,...,) based on the Liouville coupling equation is considered. The evolution operator U = exp(-iHt/h) for the Hamiltonian H = H-0 + V with a discrete spectrum is expressed in terms of the unperturbed operator U-(0) = exp(-iH(0)t/h) that has well-defined matrix elements. Comparison with the existing methods (Lanczos propagation and Chebychev series) displays the advantages of the new approach. (C) 2002 Published by Elsevier Science B.V.