Wien peaks and the Lambert W function

Abstract

Exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of diferent dispersion rules are given in terms of the Lambert W function. These dispersion rule dependent "Wien peaks" are compared to those wavelengths obtained in a setting independent of the dispersion rule chosen where the "peak" wavelengths are taken to be those obtained on dividing the total radiation intensity emitted from a blackbody into a given percentile. The account provides a simple yet accessible example of the growing applicability of the Lambert W function in physics.