V.M. Buchstaber, A.M. Perelomov
On the Functional Equation Related to the Quantum Three-Body Problem
The paper is published: in R.L. Dobrushin et. al. (eds) "Contemporary mathematical physics. F. A. Berezin memorial volume", AMS Transl. Ser. 2, 175 (31), Am. Math. Soc. 1996, 15-34

MSC:

39B32 Equations for complex functions, See also {30D05}

30D05 Functional equations in the complex domain, iteration and composition of analytic functions, See also {34A20, 39-XX, 58F08, 58F23}

81U10 $n$-body potential scattering theory

30D15 Special classes of entire functions and growth estimates

Abstract: In the present paper we give the general nondegenerate 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 pair interaction.

Keywords: quantum three-body problem, functional equations, algebraic addition theorem, Weierstrass zeta function, differential equations, Weierstrass P-function, meromorphic complex solutions