Poincare-invariant equations with a rising mass spectrum

In this note we shall construct, in the framework of relativistic quantum mechanics, the Poincare-invariant motion equations with realistic mass spectra. These equations describe a system with mass spectra of the form $m^2=a^2+b^2 s(s+1)$, where a and b are arbitrary parameters. Such equations are obtained by a reduction of the motion equation for two particles to a one-particle equation which describes the particle in various mass and spin states. It we impose a certain condition on the wave function of the derived equation, such an equation describes the free motion of a fixed-mass particle with arbitrary (but fixed) spin s.