  We derive from first principles the momentum exchange between a photon and a
quantum mirror upon reflection, by considering the boundary conditions imposed
by the mirror surface on the photon wave equation. We show that the system
generally ends up in an entangled state, unless the mirror position uncertainty
is much smaller than the photon wavelength, when the mirror behaves
classically. Our treatment leads us directly to the conclusion that the photon
momentum has the known value hk/2{\pi}. This implies that when the mirror is
immersed in a dielectric medium the photon radiation pressure is proportional
to the medium refractive index n. Our work thus contributes to the longstanding
Abraham-Minkowski debate about the momentum of light in a medium. We interpret
the result by associating the Minkowski momentum (which is proportional to n)
with the canonical momentum of light, which appears naturally in quantum
formulations.
