This paper considers the problem of optimal control of a multilevel quantum mechanical system with a multiple energy spectrum. The evolution of the systems considered is expressed by $i\dot U(t)=H(t) U(t)$, $U(0)=I$, where $H(t)=H\sb 0+H\sb 1(t)$ and $H\sb 1(t)$ specifies the interaction of the quantum mechanical system with the external control fields. These control fields depend on time and the set of allowed control fields is assumed to be given. For finding the optimal control the paper utilizes a theorem proved by {\it R. Brockett} [SIAM J. Appl. Math. 25, 213-225 (1973; Zbl 0272.93003)]. The theory is applied to a system with a vibrational- rotational spectrum. The initial state is $\vert V\sb 0,J,M>$ where $V\sb 0$, J and M are the vibrational, rotational and magnetic quantum numbers and the external field induces certain specified transitions. It is shown that the optimal control differs considerably from the controls used normally in physical experiments.
Reviewer: B.Burrows