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T. Nadareishvili

Publications and source records attributed to T. Nadareishvili.

7 recordsLinked to original sources
arXiv2025

Relativistic quantum entanglement in a bipartite charged scalar system

Continuous variable entanglement in a system of two interacting charged scalar mesons is studied. The mesons mutual interaction is mediated by a central symmetric Coulomb potential. We work out the difference between relativistic and non-relativistic limits on the basis of the continuous variable separability criteria and prove rigorously the following theorem for our system: While a bipartite charged scalar mesonic quantum system with centrally symmetric interaction is entangled in the relativistic regime, its non-relativistic counterpart can be separable with non entanglement.

quant-ph↗
arXiv2013

Electronic structure of nanorod of strongly prolate ellipsoidal shape

A charged particle (electron or hole) confined in nanorod of strongly prolate ellipsoidal shape is considered. The effective-mass Schrödinger equation is solved in prolate spheroidal coordinates and asymptotically exact expressions for the energy spectrum and wavefunctions are derived. It is shown that the treatment of the confinement energies is incorrect if the actual shape of ellipsoidal nanorod is not taken into account. In particular, developed earlier the approach based on the consideration of the problem in cylindrical coordinates with the use of parabolic potential leads to the incorrect expression for the energy spectrum. Rule of correlation between the states corresponding to spherical quantum dot and nanorod of strongly prolate ellipsoidal shape is suggested and an appropriate energy correlation diagram is constructed. The correlation diagram is in complete qualitative and quantitative agreement with the energy diagram obtained by numerical solution of the Schrödinger equation in spheroidal coordinates.

cond-mat.mes-hall↗
arXiv2009

Generalization of Hypervirial and Feynman-Hellmann Theorems for Singular Potentials

Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is performed for most general second order differential equation, which involves all physically interesting cases, as Schrodinger and Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.

hep-th↗
arXiv2009

Some Problems of Self-Adjoint Extension in the Schrodinger equation

The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional solutions must be retained for definite interval of parameters, which requires performing of Self-Adjoint Extension necessarily. The "Pragmatic approach" is used and some of its consequences are considered for wide class of transitive potentials. The problems of restriction of Self-Adjoint Extension parameter are also discussed. Various relevant applications are presented as well.

math-ph↗
arXiv2006

Dirac equation and its squared form

It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.

hep-th↗
arXiv2004

Once Again On the Klein Paradox

After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown, that the separation of angular variables and reduction to radial equation is possible by using standard methods in momentum space. The kernel of the obtained radial equation differs from that of spinless Salpeter equation in bounded regular factor. That is why the equation has solutions of confined type for infinitely increasing potential.

hep-th↗