| 752 |
|
|
| 753 |
|
The Baker-Campbell-Hausdorff formula\cite{Gilmore1974} can be used |
| 754 |
|
to determine the local error of a splitting method in terms of the |
| 755 |
< |
commutator of the |
| 756 |
< |
operators(Eq.~\ref{introEquation:exponentialOperator}) associated |
| 757 |
< |
with the sub-propagator. For operators $hX$ and $hY$ which are |
| 758 |
< |
associated with $\varphi_1(t)$ and $\varphi_2(t)$ respectively , we |
| 759 |
< |
have |
| 755 |
> |
commutator of the operators associated with the sub-propagator. For |
| 756 |
> |
operators $hX$ and $hY$ which are associated with $\varphi_1(t)$ and |
| 757 |
> |
$\varphi_2(t)$ respectively , we have |
| 758 |
|
\begin{equation} |
| 759 |
|
\exp (hX + hY) = \exp (hZ) |
| 760 |
|
\end{equation} |
