On a general way of two-particle problem reduction
  The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the Maupertuis least action principle. The proposed method is verified for known problems in two-particle problems in classical mechanics, as well as in non-relativistic and relativistic quantum mechanics. 
A.B. Arbuzov, T.V. Kopylova, A.B. Zhunisbayev
hep-ph