Abstract
A modification of the well-known Lanczos algorithm is described that adapts the method to explicitly time-dependent solutions of the Schrodinger equation. This technique possesses the desirable feature of variable time-step integration, thus eliminating the difficulties associated with fixed time-step integration schemes. Results are presented for a one-dimensional system: the so-called soft Coulomb potential in the presence of a harmonic electromagnetic field. It is demonstrated that the Lanczos propagation scheme can be efficiently and accurately used from the perturbative limit to the strong-field limit.
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