  We examine random matrix systems driven by an external field in view of
optimal control theory (OCT). By numerically solving OCT equations, we can show
that there exists a smooth transition between two states called "moving bases"
which are dynamically related to initial and final states. In our previous work
[J. Phys. Soc. Jpn. 73 (2004) 3215-3216; Adv. Chem. Phys. 130A (2005) 435-458],
they were assumed to be orthogonal, but in this paper, we introduce orthogonal
moving bases. We can construct a Rabi-oscillation like representation of a
wavpacket using such moving bases, and derive an analytic optimal field as a
solution of the OCT equations. We also numerically show that the newly obtained
optimal field outperforms the previous one.
