Methods of cumulative quantum mechanics for describing the interaction of electromagnetic fields with matter in Vysikaylo large standing nanoscale excitons: Hydrogen-like atoms, molecules, surfaces, and twinkling crystals
Year: 2025
Type: article
Abstract: Using cumulative quantum mechanics (CQM) and the method of generalized mathematical transfer (MGMT), we analytically study quantum nanometer cumulative-dissipative structures (CDS) and the forces arising within them, which focus nanostructures into regular, fractalized systems—cumulative-dissipative standing hydrogen-like excitons (atoms, molecules, lines, surfaces) and flickering crystals we discovered for the first time. (1) We demonstrate the formation of Vysikaylo standing excitons on permittivity [ε(r)] inhomogeneities in diamond in the nanoscale regions of foreign atoms. (2) For the first time, we solve the problem of measuring ε(r) profiles in inhomogeneous nanoscale structures using Raman spectra (RS) [with an accuracy of up to 99.9% for ε(r) and a step of up to 0.3 nm depending on the distance from the impurity atom (boron)]. (3) Using our theory of Vysikaylo standing excitons, we explain the experimental observation of the degeneracy of electron spectra in standing excitons with respect to the principal quantum number n and n−1/2. By comparing the theory and experimental observations of RS in diamonds doped with boron, we solve the problem (that we formulated previously) between the de Broglie hypothesis and the classical new quantum mechanics of Dirac (which limits the ψ-functions, or prohibits symmetric de Broglie half-waves in spherically and cylindrically symmetric quantum resonators) in favor of the de Broglie hypothesis. Based on the works of Wannier and Mott, we refine the definition of the permittivity of nanocrystals as a coefficient in electric potentials [U(r) → ε(r)U(r)] rather than electric fields [D(r) = ε(r)E(r)]. We construct the most complete theory of the chemical doping of crystals (using the example of group IV crystals doped with group III and V atoms). For the first time, we raise the question of the quantum cleaning of crystals or the accumulation of dopant atoms.
DOI: 10.1063/5.0256431
Author: Philipp I. Vysikaylo
Institution: Russian Academy of Sciences
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411211957