Exact two-magnon solutions of the one-dimensional isotropic Heisenberg model and string hypothesis

By means of the exact solution of the Schrodinger equation the eigenfunctions and eigenvalues of the energy for two-magnon states in the one-dimensional isotropic Heisenberg spin chain of N spins-1/2 were found. It is shown that symmetrical and antisymmetrical complex solutions have different K-dependences of the energy. Exact values of the quasi-momentum for both branches are compared with a string hypothesis prediction and solutions of the Bethe ansatz equations. With the help of the obtained solutions it was shown that resonance absorption leads to a change in momentum of the existing magnon and excitation of the magnon whose momentum is different from the absorption momentum.