Peculiarities in the Structure of Two-Particle States within the   Bethe-Salpeter Approach
  The two-fermion bound system is an attractive subject of atomic and sub-atomic physics. Despite these systems are rather simple the study of two-particle bound states is challenging and still remains a source of progress in quantum theory. Here we present a new method of solving the Bethe Salpeter equations for the bound states of spinor particles by using the expansion of the vertex functions over the complete set of four-dimensional hyperspherical harmonics. Within this method the BS equation is treated in a ladder approximation for the cases of scalar, pseudoscalar and vector meson exchanges with corresponding form factors. This method is shown to be effective and stable. 
S.M. Dorkin (MSU Dubna branch), S.S. Semikh (JINR Dubna), M. Beyer (U   Rostock), L.P. Kaptari (JINR Dubna)