Nonlinear Schrödinger equation and classical-field description of thermal radiation
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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.
KeywordsThermal 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
Funding was provided by the Tomsk State University competitiveness improvement program.
- W E Lamb and M O Scully Polarization, Matter and Radiation. Jubilee volume in honour of Alfred Kasiler (Paris: Press of University de France) p 363 (1969)Google Scholar
- O Klein, Y Nishina The Oskar Klein Memorial Lectures: 1988–1999 1 253 (2014)Google Scholar
- S A Rashkovskiy Quantum Stud. Math. Found. 3 (2) 147 (2016)Google Scholar
- S A Rashkovskiy Proc. SPIE. 9570, The Nature of Light: What are Photons? VI 95700G (2015)Google Scholar
- S A Rashkovskiy Prog. Theor. Exp. Phys. 123A03 (2015)Google Scholar
- S A Rashkovskiy Quantum Stud. Math. Found. 4 (1) 29 (2017)Google Scholar
- S A Rashkovskiy Prog. Theor. Exp. Phys. 013A03 (2017)Google Scholar
- S A Rashkovskiy arXiv:1603.02102 [physics.gen-ph] (2016)
- L D Landau and E M Lifshitz The Classical Theory of Fields Vol 2, 4th edn. (Butterworth-Heinemann) (1975)Google Scholar
- V B Berestetskii, E M Lifshitz and L P Pitaevskii Quantum Electrodynamics, Vol 4, 2nd edn. (Butterworth-Heinemann) (1982)Google Scholar