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.
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 1 Sep 2016|
- Exponential splitting
- Numerical analysis
- Schrödinger equation
ASJC Scopus subject areas
- Physics and Astronomy(all)