TITLE TIME-DEPENDENT APPROACH FOR QUANTUM DYNAMICS OF IONS AND EXOTIC SYSTEMS IN EXTERNAL FIELDS AUTHORS Vladimir S. Melezhik AFFILIATIONS temporary (till June 1999):\ Physique Nucleaire Theorique et Physique Mathematique, C.P.229, Universite Libre de Bruxelles, B 1050 Brussels, Belgium permanent address: Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russian Federation SUMMARY A non-perturbative approach is developed for the multidimensional time-dependent Schreadinger equation. With this method a few results have been obtained recently for simple electronic and muonic systems in strong external fields. The method efficiency has also been developed in application to the Coulomb breakup of exotic "halo" nuclei in collisions with heavy targets.