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

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.

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