Volume 49, Issue 3
Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles

J. Math. Study, 49 (2016), pp. 259-292.

Published online: 2016-09

[An open-access article; the PDF is free to any online user.]

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• 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.

• Keywords

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

35Q75, 37N20, 83C, 83F

matian56@sina.com (Tian Ma)

showang@indiana.edu (Shouhong Wang)

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@Article{JMS-49-259, author = {Tian and Ma and matian56@sina.com and 12743 and Department of Mathematics, Sichuan University, Chengdu, P. R. China and Tian Ma and Shouhong and Wang and showang@indiana.edu and 12473 and Department of Mathematics, Indiana University, Bloomington, IN 47405, USA and Shouhong Wang}, title = {Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n3.16.04}, url = {http://global-sci.org/intro/article_detail/jms/10122.html} }
TY - JOUR T1 - Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles AU - Ma , Tian AU - Wang , Shouhong JO - Journal of Mathematical Study VL - 3 SP - 259 EP - 292 PY - 2016 DA - 2016/09 SN - 49 DO - http://doi.org/10.4208/jms.v49n3.16.04 UR - https://global-sci.org/intro/article_detail/jms/10122.html KW - Spectrum of differential operators, energy levels, Dirac operator, Weyl operator, subatomic particles. AB -

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.

Tian Ma & Shouhong Wang. (2019). Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles. Journal of Mathematical Study. 49 (3). 259-292. doi:10.4208/jms.v49n3.16.04
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