Vol. 3 No. 1 (2025)

Open Access

Article

Article ID: 2491

Cumulative quantum mechanics and the method of generalized mathematical transfer for describing the interaction of an electric field with matter in nanostructures of chemically doped diamond

by Philipp Vysikaylo

Nano Carbons, Vol.3, No.1, 2025;

We analytically (based on cumulative quantum mechanics (CQM) and the method of generalized mathematical transfer (MGMT)) study quantum nanometer cumulative-dissipative structures (CDS) and the forces arising in them, focusing nanostructures into regular, fractalized systems—cumulative dissipative standing hydrogen-like excitons (hydrogen-like atoms, molecules, lines, surfaces) and flickering crystals discovered by the author. The CQM turned out to be useful in describing “mysterious” CDS with sizes of 10⁻¹⁵–10²⁶ m. In CDS, cumulation and dissipation of masses, energies, momenta and fields occur simultaneously (or with a certain delay) and in accordance with fairly general laws (the virial theorem works). Using the CQM and MGMT, in this paper we describe cumulative and dissipative phenomena in diamonds doped with boron (atoms from group Ⅲ of the periodic table). Problems in crystals with chemical doping with foreign atoms (with their introduction into the crystal lattice) were solved. We: (1) discovered the Vysikaylo’s standing excitons formed on inhomogeneities of the permittivity −ε(r) in diamond in the nanoregion of a foreign atom; (2) for the first time we solved the problem of measuring the ε(r) profiles in inhomogeneous nanoscale structures using Raman spectra (RS) (with an accuracy of up to 99.9% of ε(r) and a step of up to 0.3 nm depending on the distance from the impurity atom (boron)); (3) based on our theory of the Vysikaylo’s standing excitons, we prove the observation in the experiments described in the literature of degeneracy of the electron spectra in standing excitons with respect to the principal quantum number n and n-1/2. Comparing the theory and experimental observations of RS in diamonds doped with boron, we solve (formulated by us earlier) the problem between the de Broglie hypothesis and the classical new quantum mechanics of Dirac (which limits the ψ-functions-prohibits symmetric de Broglie half-waves in spherically and cylindrically symmetric quantum hollow resonators) in favor of the de Broglie hypothesis. Based on the works of Vanier and Mott, we have refined 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 have constructed the most complete theory of chemical doping of crystals (using the example of crystals of group IV elements with atoms of groups Ⅲ and V from the periodic table. For the first time, the question of quantum cleaning of crystals or cumulation of dopant atoms to each other has been raised.