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Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles

Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles
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Year:    2016

Author:    Tian Ma, Shouhong Wang

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 259–292

Abstract

Motivated by the Bohr atomic model, in this article we establish a mathematical theory to study energy levels, corresponding to bounds states, for subatomic particles. We show that the energy levels of each subatomic particle are finite and discrete, and corresponds to negative eigenvalues of the related eigenvalue problem. Consequently there are both upper and lower bounds of the energy levels for all subatomic particles. In particular, the energy level theory implies that the frequencies of mediators such as photons and gluons are also discrete and finite. Both the total number $N$ of energy levels and the average energy level gradient (for two adjacent energy levels) are rigorously estimated in terms of certain physical parameters. These estimates show that the energy level gradient is extremely small, consistent with the fact that it is hard to notice the discrete behavior of the frequency of subatomic particles.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v49n3.16.04

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 259–292

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Spectrum of differential operators energy levels Dirac operator Weyl operator subatomic particles.

Author Details

Tian Ma

Shouhong Wang

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