# Lyddane-Sachs-Teller relation

In condensed matter physics, the Lyddane-Sachs-Teller relation (or LST-relation) determines the ratio of the natural frequency of longitudinal acoustic lattice vibrations (phonons) ($\omega_L$) of an ion crystal to the natural frequency of the transverse optical lattice vibration ($\omega_T$) for k=0 which equals the ratio of the static permittivity $\varepsilon_{st}$ (Often also $\varepsilon(0)$) for the permittivity for frequencies in the visible range $\varepsilon_{\infty}$ (often also $\varepsilon(\omega_s)$).[1]
$\frac{\omega_L^2}{\omega_T^2} = \frac{\varepsilon_{st}}{\varepsilon_{\infty}}$