Quantum Mechanics/Blackbody Radiation

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body). It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.

Considering a cavity at temperature

$T$

in radiation equilibrium, the volume of the cavity is

$V=L^3$

, the energy density (energy per unit volume and frequency)

$u(\omega )$

. Here

$u(\omega )\mathrm{d}\omega$

expresses the energy per unit volume in the interval

$[\omega ,\omega +\mathrm{d}\omega ]$

. Classically, the situation is described by the Rayleigh–Jeans law

$u(\omega )=\frac{k_{B}T}{{\pi }^2{c}^3}{\omega }^2$

.One can easily make this plausible by considering standing plane waves in a cavity with reflecting metal walls.

Where L is defined as ____ and

Where u($\omega$) is defined as ____ and

Where k is defined as ____ and

Where B is defined as ____ and

Where c is defined as ____ and

Where $\omega$ is defined as ____