POINT INTERACTIONS IN QUANTUM MECHANICS

Models of point interactions that approximate the real interactions of atomic particles in quantum mechanics are considered. In a one-point one-dimensional system, states are studied taking into account the eigenfield and a non-stationary problem is solved. The concept of a "point cluster" is introduced - a complex of charges that, at zero size, create the possibility of localization of a test particle in a region of finite size. An integral model of point interaction is proposed. States in three-dimensional two-point systems with "local isotropy" are studied.