the wave function, then and it is straight forward to show that the constraint Eq.() leads directly to: in place of . This conforms with the earlier claim on the vanishing of the relative energy in the c.m. frame made in conjunction with the TBDE. In the second choice the c.m. value of the relative energy is not defined as zero but comes from the original generalized mass shell constraints. The above equations for the relative and constituent four-momentum are the relativistic analogues of the non-relativistic equations , , . Covariant eigenvalue equation for internal motion Using Eqs.(),(),(), one can write in terms of and where Eq.() contains both the total momentum [through the ] and the relative momentum . Using Eq. (), one obtains the eigenvalue equation so that becomes the standard triangle function displaying exact relativistic two-body kinematics: With the above constraint Eqs.() on then where . This allows writing Eq. () in the form of an eigenvalue equation having a structure very similar to that of the ordinary three-dimensional nonrelativistic Schrödinger equation. It is a manifestly covariant equation, but at the same time its three-dimensional structure is evident. The four-vectors and have only three independent components since The similarity to the three-dimensional structure of the nonrelativistic Schrödinger equation can be made more explicit by writing the equation in the c.m. frame in which , , . Comparison of the resultant form with the time independent Schrödinger equation makes this similarity explicit. The two-body relativistic Klein–Gordon equations A plausible structure for the quasipotential can be found by observing that the one-body Klein–Gordon equation takes the form when one introduces a scalar interaction and timelike vector interaction via and . In the two-body case, separate classical and quantum field theory arguments show that when one includes world scalar and vector interactions then depends on two underlying invariant functions and through the two-body Klein–Gordon-like potential form with the same general structure, that is Those field theories further yield the c.m. energy dependent forms and ones that Tododov introduced as the relativistic reduced mass and effective particle energy for a two-body system. Similar to what happens in the nonrelativistic two-body problem, in the relativistic case we have the motion of this effective particle taking place as if it were in an external field (here generated by and ). The two kinematical variables and are related to one another by the Einstein