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 - <p style="text-align: justify;">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.</p>