Matrix t-distribution

In condensed matter physics, the Lyddane-Sachs-Teller relation (or LST-relation) determines the ratio of the natural frequency of longitudinal optical 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 ${\epsilon }_{st}$ (Often also $\epsilon (0)$) for the permittivity for frequencies in the visible range ${\epsilon }_{\mathrm{\infty }}$ (often also $\epsilon ({\omega }_s)$).

$\frac{{\omega }_L^2}{{\omega }_T^2}=\frac{{\epsilon }_{st}}{{\epsilon }_{\mathrm{\infty }}}$

The Lyddane-Sachs-Teller relation is named after the physicists R. H. Lydanne, Edward Teller, and R. G. Sachs.

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