Symplectic time-average propagators for the Schrodinger equation with a time-dependent Hamiltonian

[EN] Several symplectic splitting methods of orders four and six are presented for the step-by-step time numerical integration of the Schrodinger equation when the Hamiltonian is a general explicitly time-dependent real operator. They involve linear combinations of the Hamiltonian evaluated at some intermediate points. We provide the algorithm and the coefficients of the methods, as well as some numerical examples showing their superior performance with respect to other available schemes. Published by AIP Publishing.
The authors acknowledge Ministerio de Economia y Competitividad (Spain) for financial support through Project Nos. MTM2013-46553-C3 and MTM2016-77660-P (AEI/FEDER, UE). Additionally, A.M. has been partially supported by the Basque Government (Consolidated Research Group No. IT649-13).