Thermal radiation between parallel conducting plates ($u(\omega )=\hslash {\omega }^2/[2\pi c^{2}d(e^{\hslash \omega /(k_{\mathrm{B}}T)}-1)]$)

Two wide perfect-conductor plates separated by $d$ support a gapless transverse electromagnetic mode whose electric field is normal to the plates. At $\omega \ll c/d$, multiply the single-polarization two-dimensional photon density of states by $\hslash \omega$ and the Bose-Einstein distribution to get the title's spectrum. This is a low-frequency statement; it need not describe the full thermal spectrum if thermally populated higher branches cross their cutoffs.