Другие журналы
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Ruckaya
Influence of degeneracy of energy levels on possibility of using the method of density functional in the case of low-dimensional systems
Engineering Education # 07, July 2012 DOI: 10.7463/0712.0435255 The author considers nanoscale systems of noninteracting fermions with cylindrical symmetry (quantum wires) which are in the simplest rectangular confining potential. It was shown that for low-dimensional quantum systems, the degeneracy of levels is primarily determined by the symmetry of the problem, and - depending on the type of building - not only degeneration caused by the presence of axial symmetry is possible, but also accidental degeneracy. Thus, the state with the same energy corresponds to different spatial distributions of electrons, which leads to divergence of results for electron density, which determines, in particular, system response to external stimuli. It follows that the usual method for estimating reliability of theoretical analysis results - comparison of energy performance characteristics – does not to allow judge how close to reality the result of calculating the electron density is.
Scaling relations in quantum multicomponent systems
Engineering Education # 08, August 2012 DOI: 10.7463/0812.0435303 This paper considers the uniqueness of solution to the variational problem in the method of density functionals. The authors investigated the scaling relations that arise in systems containing two types of particles, as well as in systems of charged particles in an electric field created by an outward charge. The possibility of using the virial theorem was studied. It is shown that for quantum systems of charged particles in the field of distributed charge the well-known relation is not executed; this relation connects average values of the kinetic energy of the system, of potential energy of particle interaction with the external field and with each other.
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