Two-magnon states of the one-dimensional isotropic Heisenberg model with free boundary conditions

By solving the Schrödinger equation the eigenfunctions and eigenvalues of the energy of two-magnon states in the one-dimensional isotropic Heisenberg model $S=1/2$ with free boundary conditions were found. The obtained solutions are single-parametrical unlike the two-parametrical solutions of the model with cyclic boundary condition. The amplitudes of the wave functions of the coupled two-magnon states have exponential dependence on both the distance between reversed spins, and the coordinate of the center of the complex. This leads to the localization of the low energy complexes at the ends of the ferromagnetic chain.