  This work is devoted to the investigation of possibility of controlling of
ions motion inside Paul trap. It has been shown that by proper selection of the
parameters of controlling electric fields, stable localization of ions inside
Paul trap is possible. Quantum consideration of this problem is reduced to the
investigation of the Mathieu-Schrodinger equation. It has been shown that
quantum consideration is appreciably different from classical one that leads to
stronger limitations of the values of the parameters of stable motion.
Connection between the problem under study and the possibility of experimental
observation of quantum chaos has been shown.
