MOV is a sintered polycrystalline ceramic based on zinc oxide (ZnO) and small amounts of other metallic oxides (additives) usually applied to the manufacturing of surge protective devices for overvoltage protection at all power system voltage classes. Nowadays surge arresters combine a complex metal oxide varistor (MOV) technology inside a polymeric housing. A dependence of the energy spectrum on the effective mass when it is a different constant inside and outside of the ellipsoid is addressed. An importance of the actual shape of ellipsoidal potential well for calculation of the energy spectrum for the trapped particle is shown. The calculated energies are in good qualitative and quantitative agreement with the results obtained earlier for the infinitely high ellipsoidal potential well via a numerical solution of the quasiradial and quasiangular equations. The obtained equation is solved numerically and algebraically. This allows us to obtain the transcendental equation for the energy levels by equating the quasiradial wave function and its derivative on the surface of ellipsoid. We demonstrate that quasiangular wave functions inside and outside of the potential well coincide on the entire surface of strongly prolate ellipsoid if separation parameters are chosen appropriately. In the case when a distance R between foci is large and accordingly R − 1 is small, the asymptotic solutions of quasiradial and quasiangular equations in prolate spheroidal coordinates are found. (2).Ī charged particle confined in a strongly prolate ellipsoidal shaped finite potential well is studied. ![]() The bound states of these confined geometries correspond to ( α, β) real and positive, α and β being linked by α 2 +β 2 =ν 2due to Eq. The Schrödinger equation of a particle of mass m in the confined geometries considered here reads, in terms of the reduced variable ξ= z/ R for quantum wells, ξ → =(| ρ → |/R,ϕ) for cylindrical wires and ξ → =(| r → |/R,θ,ϕ) for spherical dot, as ψ( ξ → )=0with ν( ξ)= α 2 for | ξ → |1. Let us now outline how we have derived the above results. From this parameter ν, we can already note that, as the physical scale for the barrier height is ℏ 2/2 mR 2, a given barrier V between two semiconductors can appear as Derivation The infinite barrier limit corresponds to ν infinite. From R and V, we can construct the dimensionless parameter ν which rules all the physics of these finite barrier problems, namely V=ℏ 2 ν 2 /2mR 2 ![]() And, of course, with a given relative abundance of elements, a mass density can be computed.We consider a particle of mass m confined in a sphere or cylinder of radius R or in a quantum well of width 2 R, the energy barrier being V. This will be valuable in obtaining more information about the atmospheres of stars in general, and quasi-stellar objects and X-ray sources in particular, as well as local density variations in the atmosphere of the sun. Astrophysical observations of effective maximum bound states andor maximum distinct levels will enable one to calculate an ion-number density in the source of absorption or emission lines. The effect of screening on the lowering of the ionization potential of an atom is illustrated by the calculation of the observed ionization potential of hydrogen as accurately as it is calculated by more elaborate methods. The concepts and results introduced here also resolve the problem of the intensity drop of hydrogen lines in the solar photosphere and chromosphere and in very low temperature hydrogen in laboratory measurements. The problem of a maximum bound principal quantum number or a finite number of screened Coulomb states has been resolved the screened Coulomb potential yields at least as many bound states as the Coulomb potential. Some numerical solutions of the Schrodinger equation with the complete screened Coulomb potential CSCP have been presented with tables and graphs of quantum numbers lambdasubscripts n, l and relative normalizations phisubscripts n, l lambda.
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