Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles (Journal of Mathematical Study, 2022)
Motivated by the Bohr atomic model, in this article we establish a mathematicaltheory to study energy levels, corresponding to bounds states, for subatomicparticles. We show that the energy levels of each subatomic particle are finite anddiscrete, and corresponds to negative eigenvalues of the related eigenvalue problem.Consequently there are both upper and lower bounds of the energy levels for all subatomicparticles. In particular, the energy level theory implies that the frequencies ofmediators 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 energylevels) are rigorously estimated in terms of certain physical parameters. These estimatesshow that the energy level gradient is extremely small, consistent with the factthat it is hard to notice the discrete behavior of the frequency of subatomic particles.