The Liouville coupling equation for the calculation of evolution operators

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/ℏ) for the Hamiltonian H=H0+V with a discrete spectrum is expressed in terms of the unperturbed operator U(0)=exp(−iH0t/ℏ) that has well-defined matrix elements. Comparison with the existing methods (Lanczos propagation and Chebychev series) displays the advantages of the new approach.