  A nonrelativistic equation for the system of two interacting particles within
the framework of a model with noncommuting operators of coordinates and momenta
of different particles is proposed, and a self-consistent system of equations
for the wave function of every quantum state is deduced. Solutions for the
lowest states of a hydrogenlike atom are found, and the comparison with
analogous solutions of the Klein-Gordon equation for the relativistic spinless
problem is performed. In the case where the size of a two-particle system and
the Compton wavelengths of particles forming it are of the same order, the
essential differences with solutions of the Schr\"{o}dinger nonrelativistic
equation are revealed.
