Noncommutative Derivation of the Planck's Radiation Law

The Planck's radiation law for the black body radiation spectrum was capable to explain the experimentally-measured black body spectrum. In order to get this result, Planck proposed his radiation law in a two-fold way: 1) by an ad hoc modification of the assumed connection between energy and entropy for thermal radiation; 2) by assuming that the calculation of the entropy of an oscillator in thermal equilibrium with radiation is carried out by discrete units of energy. As a consequence, the energy quantization, linear in frequency, was thus introduced into physics. However, the energy quantization of the simple harmonic oscillator was originally postulated by Planck in an incomplete way, i.e., the ground state energy was assumed to be null. Of course, this issue has been solved in different ways over time, even by him. Despite this, we propose an alternative way to restore the non-null ground state energy of the harmonic oscillators at noncommutative(NC) framework, where, how will be shown, the non-null ground state energy naturally arises as a NC contribution. With this approach, the Planck's quantum theory is updated and, consequently, becomes compatible with the Quantum Mechanics inaugurated in 1925.

Keywords
Blackbody radiation; Planck's radiation law; Planck's postulate; ⋆-product; Noncommutative theory