In a 1D ferromagnet, collective spin precession forms magnons.
Dispersion omega(k) = 2JS(1-cos k): quadratic near k=0 (massive magnon), maximum at k=pi (4JS).
Group velocity v_g = dw/dk = 2JS sin k gives the wave packet speed.
Phase velocity v_p = omega/k differs, causing dispersion. Click the dispersion plot to select a mode.