For a two-dimensional Coulomb system of three charged particles, among which two particles are identical and the third particle is of different nature, we study the conditions of existence for symmetric and antisymmetric bound energy states (conditions of stability) in the masscharge (m, Z) plane. High-precision three-body numerical calculations based on a stochastic variational method with Gaussian bases are performed. Several anomalous effects in the behavior of the characteristic distances between particles are revealed, and the nonzero quadrupole moment is found in a two-dimensional polar-symmetric field. The systematic comparison of the results for two-and three-dimensional systems is performed. The values of energy and size, the density distributions, and the correlation functions for the various reference three-particle systems are obtained. K e y w o r d s: three charged particles, two-dimensional systems, stability, variational method, structural functions

A complete account of correlations has been shown to make δ-like repulsive interaction potentials inefficient for any N -particle quantum system in the D-dimensional space with D ≥ 2.K e y w o r d s: N -particle system, D-dimensional space, δ-like interaction potential, energy spectrum, wave function.

Медико-біологічні аспекти підготовки спортсменівУкраїнський журнал медицини, біології та спорту -Том 4, № 6 (22)

It is shown that the Schrödinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schrödinger equation.