Black-body radiation
Ultraviolet Catastrophe
Wein (1889)
\(E=\sigma T^4\), Stefan-Boltzman Law. \(\sigma=5.67\cdot10^8\). \(U(\nu,T)=A\nu^3\exp(-\beta\nu/T)\)
Planck (1900)
Oscillators \(\nu\) are quantized by energy such that \(E=n\hbar\nu\), \(n\in\mathbb{N}\).
- \(U(\nu,T)=\frac{8\pi\nu^2}{c^3}\frac{\hbar\nu}{\exp(\hbar\nu/(k_BT))-1}\)