A SIMPLIFIED APPROACH TO OPTIMALLY CONTROLLED QUANTUM DYNAMICS

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous clas sical control technique reported previously [J. Botina, H. Rabitz, and N. Rahman, J. Chem. Phys. 102, 226 (1995)]. Quantum Lagrange multipli er functions are used to preserve a chosen subset of the observable dy namics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of ti me. This is a considerable simplification over traditional quantum opt imal control theory [S. Shi and H. Rabitz, Comp. Phys. Comm. 63, 71 (1 991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum con trol to meet a physical objective. A family of such simplified formula tions is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model p roblem for selective unimolecular reaction induced by an external opti cal electric field. (C) 1996 American Institute of Physics.