Planck's blackbody radiation law: Presentation in different domains and determination of the related dimensional constants
In this paper the Planck function is derived in the frequency domain using the method of oscillators. It is also presented in the wavelength domain and in the wave number domain. The latter is mainly used in spectroscopy for studying absorption and emission by gases. Also the power law of Stephan and Boltzmann is derived for these various domains. It is shown that this power law is generally independent of the domain in which the Planck function is presented. A formula for the filtered spectrum is also given and expressed in the sense of the power law of Stefan and Boltzmann. Furthermore, based on Wien's displacement relationship, it is argued that the wavelength at which the maximum of the Planck function presented in the wavelength domain occurs differs from that of the maxima of the other domains by a factor of 1.76. As Planck determined his elementary quantum of action, eventually called the Planck constant, and the Boltzmann constant using Wien's displacement relationship formulated for the wavelength domain, it is shown that the values of these fundamental constants are not affected by the choice of domain in which the Planck function is presented. Finally, the origin of the Planck constant is discussed.