Coefficients of several symplectic splitting methods
of order 4 and 6 for the time integration of the
Schrödinger equation when the Hamiltonian is
time-dependent
In the paper
S. Blanes, F. Casas and
A. Murua. Symplectic time-average propagators for the Schrödinger equation with a time dependent Hamiltonian. The Journal of Chemicall Physics 146
(2017), 114109
different fourth- and
sixth-order symplectic splitting methods are obtained and tested
on a pair of examples. Although we list in the Appendix all the
coefficients (with 12 digits), we collect them also here, this
time with more accuracy. The methods are called
SM_8^{[4]}, SM_{11}^{[6]} and SM_{11}^{[8]}, respectively, and
their coefficients can be found here.
Moreover, we include next some Matlab codes implementing the
symplectic splitting methods presented in the paper for the
academic example analyzed there. The file readme
contains all the necessary information, whereas the
corresponding codes are included in:
The (compressed) folder AdditionalFiles
contains some other codes needed to compare the performance of
the new methods. In order to work properly, they have to be
located in the folder where the exact solution is evaluated.