In condensed matter physics, the Lyddane–Sachs–Teller relation (or LST relation) determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) ( ω ω LO ) of an ionic crystal to the natural frequency of the transverse optical lattice vibration ( ω ω TO ) for long wavelengths (zero wavevector). The ratio is that of the static permittivity ε ε st to the permittivity for frequencies in the visible range ε ε ∞ ∞ .