On the functional equation related to the quantum three-body problem
  In the present paper we give the general solution of the functional equation $$ (f(x)+g(y)+h(z))^2 = F(x)+G(y)+H(z), x+y+z=0 $$ which is related to the exact factorized ground-state wave function for the quantum one-dimensional problem of three different particles with pairwise interaction. 
V.M. Buchstaber and A.M. Perelomov