Interactions of point clusters

Pointwise interactions are considered. Such interactions approximately describe real interactions of atomic particles in quantum mechanics. The notion of 'pointwise cluster' is introduced: it is a compound of charges that enable the localization of a probe particle in the region of finite size. States in one-dimensional systems are considered, and in three-dimensional systems with 'local isotropy' as well. States of poitwise systems with non-zero, including fractional, orbital moments are studied.