Thermal fluctuations of a lipid bilayer governed by the Helfrich Hamiltonian: H = ∫[(κ/2)(∇²h)² + (σ/2)|∇h|²]dA. Mode amplitudes ⟨|h_q|²⟩ = k_BT/(κq⁴ + σq²). Bending rigidity κ and surface tension σ control the fluctuation spectrum.