Problem of two magnons in a Bethe chain

The linear chain of spins $1/2$ with exchange interaction between nearest neighbors is considered. All eigenfunctions of two magnons are found in such a chain. A structure of long wave exitations and of exitations with wave vector equals to $\pi$ are clarified. The totality of this system of functions is proved. In other respects the work is an interpretation of the first half of the Bethe paper [1] of 1931.