  We present a simple method to expedite simulation of quantum wave-packet
dynamics by more than a factor of $2$ with the Strang split-operator
propagation. Dynamics of quantum wave-packets are often evaluated using the the
\emph{Strang} split-step propagation, where the kinetic part of the Hamiltonian
$\hat{T}$ and the potential part $\hat{V}$ are piecewise integrated according
to $e^{- i \hat{H} \delta t} \approx e^{- i \hat{V} \delta t/2} e^{- i
\hat{T}\delta t} e^{- i \hat{V} \delta t/2}$, which is accurate to second order
in the propagation time $\delta t$. In molecular quantum dynamics, the
potential propagation occurs over multiple coupled potential surfaces and
requires matrix exponentiation for each position in space and time which is
computationally demanding. Our method employs further splitting of the
potential matrix $\hat{V}$ into a diagonal space dependent part
$\hat{V}_{D}(R)$ and an off-diagonal time-dependent coupling-field
$\hat{V}_{OD}(t)$, which then requires only a single matrix exponentiation for
each time-step, considerably reducing the calculation time even in the simplest
two-surface interaction ($\sim$70\% reduction observed in potential propagation
time). We analyze the additional error due to the potential splitting and show
it to be small compared to the inherent error associated with the
kinetic/potential splitting.
