Selective control of the observables in the ensemble of quantum mechanical molecular systems

A new approach to synthesize algorithms for selective control of the observables in quantum mechanical systems in the presence of additional constraints during the whole period of control is proposed. Analytic results of achieving the goal of control under some additional assumptions were obtained. It was demonstrated that the error in achieving the goal of control is proportionate to the error in prescribing the initial state of system and the error in realizing the control action. Numerical results for the problem of selective control for energy of hydrogen molecules $({\mathrm{H}}_2)$ with different isotopes are represented. The proposed algorithms are easy to design.