We build efficient and unitary (hence stable) methods for the solution of the linear time-dependent Schrödinger equation with explicitly time-dependent potentials in a semiclassical regime. The Magnus–Zassenhaus schemes presented here are based on a combination of the Zassenhaus decomposition (Bader et al. 2014 Found. Comput. Math. 14, 689–720. (doi:10.1007/s10208-013-9182-8)) with the Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical experiments.
- Received October 22, 2015.
- Accepted August 15, 2016.
- © 2016 The Author(s)
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