We demonstrate that the intensity of the energy emission
obtained from the Joule-Lenz law applied to the case of a single free-electron
particle or a harmonic oscillator does not depend on the change of size of the
corresponding energy interval () and time interval () because the ratio of？？to？？representing the emission rate remains
constant. For a free electron, this property holds on
condition the calculations of？？and？？refer to the states having a sufficiently
large quantum index n.
References
[1]
Lass, H. (1950) Vector and Tensor Analysis. McGraw-Hill, New York.
[2]
Matveev, A.N. (1964) Electrodynamics and the Theory of Relativity, Izd. Wyzszaja Szkola, Moscow. (In Russian)
[3]
Olszewski, S. (2015) Non-Probabilistic Approach to the Time of Energy Emission in Small Quantum Systems. Journal of Modern Physics, 6, 1277-1288. https://doi.org/10.4236/jmp.2015.69133
[4]
Eyring, H. and Walter, J. and Kimball, G.E. (1957) Quantum Chemistry. Wiley, New York.
[5]
Slater, J.C. (1960) Quantum Theory of the Atomic Structure. McGraw-Hill, New York.
[6]
Schiff, L.I. (1968) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York.
[7]
MacDonald, A.H. (1989) Quantum Hall Effect—A Perspective. Kluwer, Milano. https://doi.org/10.1007/978-94-010-9709-3
[8]
Olszewski, S. (2016) Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions. Journal of Modern Physics, 7, 827-851. https://doi.org/10.4236/jmp.2016.78076
[9]
Olszewski, S. (2016) Semiclassical and Quantum-Mechanical Formalism Applied in Calculating the Emission Intensity of the Atomic Hydrogen. Journal of Modern Physics, 7, 1004-1020. https://doi.org/10.4236/jmp.2016.79091 (2016) Erratum to “Semiclassical and Quantum-Mechanical Formalism Applied in Calculating the Emission Intensity of the Atomic Hydrogen” [Journal of Modern Physics 7 (2016) 1004-1020]. Journal of Modern Physics, 7, 2314-2315. https://doi.org/10.4236/jmp.2016.716199
[10]
Olszewski, S. (2017) Time Intervals of the Electron Transitions and Intensity Spectrum of the Hydrogen Atom. Journal of Computational and Theoretical Nanoscience, 14, 4086-4099. https://doi.org/10.1166/jctn.2017.6791
[11]
Olszewski, S. (2016) Quantum Aspects of the Joule-Lenz Law. Journal of Modern Physics, 7, 162-174. https://doi.org/10.4236/jmp.2016.71018
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