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We reformulate the Lanczos algorithm for quantum wave function propagation interms of variational principle. By including some basis states of previous timesteps into the variational subspace, the resultant accuracy increases byseveral orders. Numerical errors of the alternative method accumulate muchslower than that of the original Lanczos method. There is almost no extranumeric cost for the gaining of the accuracy, i.e., the accuracy increase needsno extra operations of the Hamiltonian acting on state vectors, which are themajor numeric cost for wave function propagation. A wave packet moving in a2-dimensional H\'enon-Heiles model serves as an illustration. This method issuitable for small time step propagation of quantum wave functions in largescale time dependent calculations where the operations of the Hamiltonianacting on state vectors are expensive.Comment: To appear in J. Phys.

An alternative implementation of the Lanczos algorithm for wavefunction propagation