On the functional equation related to the quantum three-body problem

TL;DR

This paper solves a key functional equation linked to the ground-state wave function of a three-particle quantum system with pairwise interactions, advancing understanding of quantum three-body problems.

Contribution

It provides the general solution to a specific functional equation associated with the quantum three-body problem, which was previously unresolved.

Findings

Derived the general solution to the functional equation.

Connected the solution to the exact ground-state wave function.

Enhanced understanding of quantum three-body interactions.

Abstract

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.