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International Journal of Theoretical Physics

, Volume 29, Issue 12, pp 1379–1392 | Cite as

Underlying probability distributions of Planck's radiation law

  • B. H. Lavenda
Article

Abstract

The derivation of Planck's radiation law can be considered as a transformation of a thermodynamic relation for black-body radiation into a fundamental relation in which the error law is the negative binomial distribution. In both limiting frequency ranges it transforms into Poisson distributions; in the Wien limit, it is the distribution of the number of photons, whose most probable value is given by Boltzmann's expression, while in the Rayleigh-Jeans limit, it is the distribution of the number of Planck oscillators. In the general case, they are Bernoullian random variables. In the Rayleigh-Jeans limit, the probability of determining the number of oscillators in a given frequency interval for a fixed value of the energy can be inverted to determining the probability of the energy for a fixed number of oscillators. The probability density is that of the canonical ensemble.

Keywords

Probability Distribution Field Theory Probability Density Elementary Particle Quantum Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • B. H. Lavenda
    • 1
  1. 1.Università degli StudiCamerinoItaly

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