An explicit form of total angular momentum eigenfunctions is found for the physical systems described by one three-dimensional space coordinate and arbitrary spin degrees of freedom. The resulting formula is usefully parametrized by the multicomponent radial wave function. The dependence on the angular coordinates is given by action of generalized spherical harmonics. The formula gives a convenient method of separation of the angular coordinates in an arbitrary one- or two-body wave equation with spin. As an example, the
method was applied to the relativistic wave equation for one Dirac and one Duffin-Kemmer
particle, proposed recently by Królikowski. A corresponding set of radial equations is derived
in the case of spherically symmetrical interaction potentials.