= Rectangular electromagnetic cavity
{title2=$\nu=\frac c2\sqrt{(l/L_x)^2+(m/L_y)^2+(n/L_z)^2}$}
A closed rectangular <perfect conductor> cavity has discrete <normal modes> selected by zero tangential <electric field> at the walls. Each <frequency> has the displayed form. With all three indices positive there are two independent <polarizations of an electromagnetic wave>; modes with exactly one zero index have one, and those with two zero indices are absent. For example the $n=0$ family can have $E_z\propto\sin(\pi lx/L_x)\sin(\pi my/L_y)$, independent of $z$. It satisfies the wall conditions because $E_z$ is normal to the $z$ faces and tangential to the side walls. Omitting such zero-index families is harmless for leading bulk <density of states>, but changes the low-<temperature> physics of a thin cavity.
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