Symplectic time-average propagators for the Schrödinger equation with a time-dependent Hamiltonian.
Several symplectic splitting methods of orders four and six are presented for the step-by-step time numerical integration of the Schrödinger 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.
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, E-46022 Valencia, Spain.
Sergio
S
Blanes
Departament de Matemàtiques and IMAC, Universitat Jaume I, E-12071 Castellón, Spain.
Fernando
F
Casas
Konputazio Zientziak eta Adimen Artifiziala Saila, Informatika Fakultatea, EHU/UPV, Donostia/San Sebastián, Spain.
Ander
A
Murua