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Derivation of Bose’s Entropy Spectral Density from the Multiplicity of Energy Eigenvalues
Version 1
: Received: 15 May 2024 / Approved: 15 May 2024 / Online: 15 May 2024 (13:25:31 CEST)
How to cite: Spalvieri, A. Derivation of Bose’s Entropy Spectral Density from the Multiplicity of Energy Eigenvalues. Preprints 2024, 2024051050. https://doi.org/10.20944/preprints202405.1050.v1 Spalvieri, A. Derivation of Bose’s Entropy Spectral Density from the Multiplicity of Energy Eigenvalues. Preprints 2024, 2024051050. https://doi.org/10.20944/preprints202405.1050.v1
Abstract
The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three dimensional continuous version of the three discrete quantum numbers, that leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose’s entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency.
Keywords
Blackbody Radiation; Bose-Einstein Distribution; Degeneracy of Energy Eigenvalues; Multiplicity of Energy Eigenvalues; Density of States
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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