  Exact analytical calculations of eigenvalues and eigenstates are presented
for quantum coupled double-well (DW) systems with Razavy's hyperbolic
potential. With the use of four kinds of initial wavepackets, we have
calculated the tunneling period $T$ and the orthogonality time $\tau$ which
signifies a time interval for an initial state to evolve to its orthogonal
state. We discuss the coupling dependence of $T$ and $\tau$, and the relation
between $\tau$ and the concurrence $C$ which is a typical measure of the
entanglement in two qubits. Our calculations have shown that it is not clear
whether the speed of quantum evolution may be measured by $T$ or $\tau$ and
that the evolution speed measured by $\tau$ (or $T$) is not necessarily
increased with increasing $C$. This is in contrast with the earlier study [V.
Giovannetti, S. Lloyd and L. Maccone, Europhys. Lett. {\bf 62} (2003) 615]
which pointed out that the evolution speed measured by $\tau$ is enhanced by
the entanglement in the two-level model.
