A comparison of different propagation schemes for the time dependent Schrödinger equation

C. Leforestier*, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H. D. Meyer, N. Lipkin, O. Roncero, R. Kosloff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

874 Scopus citations

Abstract

A comparison of three widely used time propagation algorithms for the time dependent Schrödinger equation is described. A typical evolution problem is chosen to demonstrate the efficiency and accuracy of the various methods on a numerical grid using a pseudo-spectral (FFT) spatial representation for scattering and bound state evolution. The methods used -second-order differencing, split operator propagation, Chebyshev polynomial expansion-are discussed in terms of their applicability to various classes of dynamic problems. A new method is introduced which is based upon a low-order Lanczos technique. This method appears to offer an accurate and flexible alternative to the existing techniques. Overall the Chebyshev method is recommended for time independent potentials and the Lanczos method for time dependent potentials.

Original languageEnglish
Pages (from-to)59-80
Number of pages22
JournalJournal of Computational Physics
Volume94
Issue number1
DOIs
StatePublished - May 1991
Externally publishedYes

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