A Fabry-Pérot cavity with a movable mirror couples photon number n̂ to mirror position x̂ via H = −g₀x̂n̂. Driving the cavity red-sideband (Δ = −ωm) enables sideband cooling: each absorbed photon removes one phonon, reducing the mirror's thermal motion toward the quantum ground state. The cooperativity C = 4g²n̄/κΓ determines cooling efficiency, and the final phonon number n̄f ≈ (κ/4ωm)² in the resolved-sideband regime.