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Indian Journal of Physics

, Volume 92, Issue 3, pp 289–302 | Cite as

Nonlinear Schrödinger equation and classical-field description of thermal radiation

  • Sergey A. Rashkovskiy
Original Paper

Abstract

It is shown that the thermal radiation can be described without quantization of energy in the framework of classical field theory using the nonlinear Schrödinger equation which is considered as a classical field equation. Planck’s law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived without using the concept of the energy quanta. It is shown that the spectral energy density of thermal radiation is apparently not a universal function of frequency, as follows from the Planck’s law, but depends weakly on the nature of atoms, while Planck’s law is valid only as an approximation in the limit of weak excitation of atoms. Spin and relativistic effects are not considered in this paper.

Keywords

Thermal radiation Hydrogen atom Classical field theory Light–atom interaction Deterministic process Nonlinear Schrödinger equation Planck’s law Einstein A-coefficient Statistical interpretation 

PACS Nos.

03.65.Ta 03.65.Sq 

Notes

Acknowledgements

Funding was provided by the Tomsk State University competitiveness improvement program.

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Copyright information

© Indian Association for the Cultivation of Science 2017

Authors and Affiliations

  1. 1.Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia
  2. 2.Tomsk State UniversityTomskRussia

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