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