  Edge magnetoplasmons arise on a boundary of conducting layer in perpendicular
magnetic field due to an interplay of electron cyclotron motion and Coulomb
repulsion. Lateral electric field, which confines electrons inside the sample,
drives their spiraling motion in magnetic field along the edge with the average
drift velocity contributing to the total magnetoplasmon velocity. We revisit
this classical picture by developing fully quantum theory of drift velocity
starting from analysis of magnetic edge channels and their electrodynamic
response. We derive the quantum-mechanical expression for the drift velocity,
which arises in our theory as a characteristic of such response and can be
calculated as harmonic mean of group velocities of edge channels crossing the
Fermi level. Using the Wiener-Hopf method to solve analytically the edge mode
electrodynamic problem, we demonstrate that the edge channel response
effectively enhances the bulk Hall response of the conducting layer and thus
increases the edge magnetoplasmon velocity. In the long-wavelength limit of our
model, the drift velocity is simply added to the total magnetoplasmon velocity,
in agreement with the classical picture.
