  We report on a quantum description of the domain wall (DW) motion under a
spin current. A bound magnon, which is the zero mode of DW, is found to play a
dominant role in DW dynamics. The bound magnon acquires its inertia by the hard
axis anisotropy and is a free particle even under the spin current. The full
transfer of spin angular momentum from the spin current to DW via the bound
magnon leads to the DW motion with the adiabatic velocity, decoupling of spin
waves from DW, and no Doppler shift in spin waves.
