arXiv subjects
Publications and source records attributed to N. N. Trunov.
We generalize the universal effective quantum number introduced earlier for centrally symmetric problems. The proposed number determines the semiclassical quantization condition for axially symmetric potentials.
We approximate given potentials by means of the specially introduced reference potentials. On the one hand their parameters may be easily found from the usual WKB integral for the given potential; on the other hand they allow a simple determination of the first correction to the usual quantization condition. Such reference potentials are introduced in special variables as some Pade approximants which lead usually to a very good results for various problems. Thus we raise the accuracy of the WKB method for a broad set of potentials without cumbersome calculations. Higher order corrections as well as the exact condition is also considered.
The exact semiclassical quantization condition represents a cumbersome series expansion, so that only the main term of it is usually taken into account. We propose a way to find next terms without new additional calculations. Results are exact for a wide class of actual potentials.
An enormous variety of quantum nanoobjects and nanosystems calls for the development of new approaches to their description and parametrization. Corresponding methods should be simple, universal enough and ensuring the retention of essential part of information at small number of parameters. A universal effective quantum number was introduced earlier and successfully used for describing centrally symmetric systems. But in most cases nanosystems own a lower symmetry. In the present article we generalize and adapt this method for such systems.
Quantum nanosystems are exremely diverse and often very complicated. That is why new methods of a simple description of such systems ensuring the retention of essential part of information at small numbers of parameters are needed. We consider several approaches to such reduced description. Besides we warn against using of one new incorrect approach.
The universal effective quantum number that determines the level ordering in arbitrary centrally symmetric potentials is defined more precisely by means of an improved variant of the semiclassical approach
We inroduce a new model for Bingham fluids with a complicated dependence of the deformation velocity on the shear stress. Specific features of the flow rate for such fluid are studied. This model embraces many special and limiting cases, for many of them analytic calculations become possible
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very wide and important class of them for which an exact condition can be constructed. The accuracy is estimated for a number of special cases
We consider liquid suspensions with dispersed nanoparticles. Using two-points Pade approximants and combining results of both hydrodynamic and molecular dynamics methods, we obtain the effective viscosity for any diameters of nanoparticles
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a dimensionless parameter which indicates high quality of the long form of the Periodic system.
We demonstrate how a certain new form of the quantization condition proposed earlier can be used outside the class of potentials for which this form ensures exact spectra. Taking this form as a base we get an improved interpolating condition for the potential wells with coinciding an + and - infinities asymptotical values. Accuracy of the above conditions is discussed.
A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the deviation of the studied potential from the supersymmetric one so that on the base of the presented method a new kind of the perturbation theory not connected with the Planck constant may be developed
Methods for simple and effective determination of reological parameters of non-Newtonian liquids are proposed
An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known estimates for the total number of the bound states in the same potential for various dimensionality. Coincidence with some known exact results is demonstrated. The effective number is used for constructing the periodical system of the atomic electron shells.