Paul Trap and the Problem of Quantum Stability

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.