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In condensed matter physics, the Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations of an ionic crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths. The ratio is that of the static permittivity ε st {\displaystyle \varepsilon _{\text{st}}} to the permittivity for frequencies in the visible range ε ∞ {\displaystyle \varepsilon _{\infty }}.
ω LO 2 ω TO 2 = ε st ε ∞ {\displaystyle {\frac {\omega _{\text{LO}}^{2}}{\omega _{\text{TO}}^{2}}}={\frac {\varepsilon _{\text{st}}}{\varepsilon _{\infty }}}}
The Lyddane–Sachs–Teller relation is named after the physicists R. H. Lyddane, Robert G. Sachs, and Edward Teller.