A 1D chain of N atoms coupled by springs. Normal-mode diagonalization gives phonon dispersion ω(k) = 2ω₀|sin(ka/2)|. Each mode is a quantum harmonic oscillator with zero-point energy ½ℏω(k). The vacuum fluctuates — even at T=0, each atom oscillates with amplitude √(ℏ/2mω(k)) summed over all modes.