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Updated: Jul 4, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Accurate time propagation for the Schrodinger equation with an explicitly time-dependent Hamiltonian
Katharina Kormann1, Sverker Holmgren, Hans O Karlsson
1Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden.
Abstract:
Several different numerical propagation techniques for explicitly time-dependent Hamiltonians are discussed and compared, with the focus on models of pump-probe experiments. The quality of the rotating wave approximation is analyzed analytically, and we point out under which circumstances the modeling becomes inaccurate. For calculations with the fully time-dependent Hamiltonian, we show that for multistate systems, with either time or space dependence in the interstate coupling, the fourth order truncated Magnus expansion can be reformulated so that no commutators appear. Our results show that the split-operator method should only be used when low accuracy is acceptable. For accurate and efficient time stepping, the Magnus-Lanczos approach appears to be the best choice.
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