Trapping and localization of particles by a potential well deepening with time

The universal mechanism of trapping and localization of sufficiently slow-speed particles by a potential well deepening with time is established on the basis of fundamental relations of classical mechanics. Such wells may be created for a wide range both charged and neutral particles (with electric or magnetic moments) by means of a controllable electromagnetic field with growing strength (up to a certain moment) but with a fixed spatial distribution. Detailed analysis of features of corresponding electromagnetic traps of particles is carried out on the visual example of the one-dimensional rectangular potential well deepening with time. Obtained results may be used in ultrahigh resolution spectroscopy of various microparticles (including atoms, molecules and ions).