Method of separating the angularcoordinates in two-body waveequations with spin

Abstract

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.