Аннотация
The processes of physical doping of nano-structured (meta-) materials are investigated. Cumulative quantum mechanics (CQM) as stated by the author was the base for the following: 1) Two types of interference and diffraction (in the center) in the hollow quantum cavities for de Broglie waves of electrons, and 2) Two types of Vysikaylo’s quantum-size effects due to polarization capture of electrons in the cavity quantum resonators. The first type of interference and, accordingly, the diffraction at the center of the cavity corresponds to the interference of de Broglie- Fresnel (sin-wave with a node in the center of the resonator). This type is used to describe the localization (accumulation) of electrons in the atom (quantum cavity with an atomic nucleus in the center of the cavity). The second type of interference and, accordingly, diffraction is called Vysikaylo – de-Broglie-Fraunhofer interference (diffraction with the antinode of the de Broglie wavelength of an electron in the center of a hollow resonators), in which ψn – the functions of an electron are indefinitely accumulated (focus polarization "mirror") towards the center of a hollow spherical or cylindrically symmetrical quantum resonator (ψn(r) ~ cos (knr)/rk). It is shown that the irregular cos- solutions in the center of the cavity, for all of the wave phenomena, are regularized by the regularized geometric factor. In the framework of CQM, the following is proved: along with the classical energy spectrum for asymmetric ψn- functions (sin-waves – harmonics) with En ~ n2 for hollow quantum resonators there are also symmetric ψn-functions (cos-waves – the fundamental tone ) with En ~ (n-1/2)2 realized in the experiments. Energy spectrum of states localized by barrier, with En>0 (metastable IQ-particle – partially open quantum dot, line or well), as in the case of En<0 (FQ- stable particle – a closed quantum dot, line or well), is determined by effective internal box dimensions (R + rind) with polarization forces, effective at the distance rind from the hollow molecule. Comparisons of the results of analytical calculations with experimental observations conclusively prove the validity of CQM for the description of quantum-size effects in the physical doping of metamaterials. For the first time it was demonstrated that in nanocomposite materials a couple of "proper function ψn – eigenenergy En» that constitutes a quantum state in the nanoworld, marked by the main quantum number n, in the mesoworld of nanocomposites physically doped by traps is replaced by two parameters: diameter of the nanocrystal – D and the resonance of the relative concentration of the modifier (traps, such as C60, 70) – ζn in the present work the self-assembly of hollow allotropic forms of carbon in resonant electrons is discussed.