  We study the scattering of an electron by a ferromagnetic domain wall of the
quantum Heisenberg-Ising model (XXZ model) with certain boundary conditions.
The spin of the electron interacts with the spins of the XXZ model by the Hund
coupling. Using the exact domain wall ground states of the XXZ model, we
analytically obtain the exact effective Schr\"odinger equation for conduction
electrons. This equation coincides with a conventional phenomenological
Schr\"odinger equation which was derived in a classical treatment of spins of a
domain wall. By solving the Schr\"odinger equation numerically, we have
calculated the transmission coefficient which is a function of the Hund
coupling and of the anisotropy of the XXZ model. It turns out that the
transmission coefficient is vanishing in the low energy limit for the electron.
