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Ovsiyuk E.,Mozyr State Pedagogical University | Veko O.,Mozyr State Pedagogical University | Amirfachrian M.,National Academy of Sciences of Belarus
Nonlinear Phenomena in Complex Systems | Year: 2012

It is shown that the Schrödinger equation with a potential in the form of a combination of three potentials Coulomb, linear and harmonic, the potential often used to describe quarkonium, is reduced to a bi-confluent Heun differential equation. The method to construct its solutions in the form of polynomials is developed, however with additional constraints in four parameters of the model, α,β,k,l. The energy spectrum looks as a modified combination of oscillator and Coulomb parts.


Ovsiyuk E.M.,Mozyr State Pedagogical University | Veko O.V.,Mozyr State Pedagogical University | Red'kov V.M.,National Academy of Sciences of Belarus
Nonlinear Phenomena in Complex Systems | Year: 2013

Lobachevsky geometry simulates a medium with special constitutive relations, Di = ε0εikEk, Bi = μ0μikHk where two matrices coincide: εik(x) = μik(x). The situation is specified in quasi-cartesian coordinates (x, y, z). Exact solutions of the Maxwell equations in complex 3-vector E+iB form, extended to curved space models within the tetrad formalism, have been found in Lobachevsky space. The problem reduces to a second order differential equation which can be associated with an 1-dimensional Schödinger problem for a particle in the external potential field U(z) = U0e2z. In quantum mechanics, curved geometry acts as an effective potential barrier with reflection coefficient R = 1; in electrodynamic context results similar to quantum-mechanical ones arise: the Lobachevsky geometry simulates a medium that effectively acts as an ideal mirror. Penetration of the electromagnetic field into the effective medium, depends on the parameters of an electromagnetic wave, frequency ω, k2 1 + k2 2, and the curvature radius ρ.


Kazmerchuk K.V.,Mozyr State Pedagogical University | Ovsiyuk E.M.,Mozyr State Pedagogical University
Ukrainian Journal of Physics | Year: 2015

The generalized relativistic Klein–Fock–Gordon equation for Cox’s non-point scalar particle with intrinsic structure is solved in the presence of external uniform magnetic and electric fields in the Minkowski space. Similar problems in the non-relativistic approximation in a closed spherical Riemann 3-space are examined. The complete separation of the variables in the system of special cylindric coordinates in a curved model is performed. In the presence of a magnetic field, the quantum problem in the radial variable is solved exactly, and the wave functions and the corresponding energy levels are found: the quantum motion in the z-direction is described by a one-dimensional Schrödinger-like equation in an effective potential, which turns out to be too difficult for the analytical treatment. In the presence of an electric field against the background of the curved model, the situation is similar: the radial equation is solved exactly in hypergeometric functions, but the equation in the z-variable can be examined only qualitatively. © K.V. KAZMERCHUK, E.M. OVSIYUK, 2015.


Ovsiyuk E.M.,Mozyr State Pedagogical University
Ukrainian Journal of Physics | Year: 2015

The relativistic theory of Cox’s scalar non-point particle with intrinsic structure in the Proca approach in external uniform magnetic and electric fields in the Minkowski space is developed. A generalized Klein–Gordon–Fock equation is derived and is detailed in the presence of uniform magnetic and electric fields. The extension of this formalism to the arbitrary Riemannian space-time background is given. For a special class of curved metrics allowing for the existence of nonrelativistic wave equations, a generalized Schrödinger-type quantum mechanical equation for Cox’s particle is derived. This generally covariant formalism is suitable in the presence of external magnetic and electric fields. It is shown that, in the most general form, the extended first-order Proca-like system of tensor equations contains non-minimal interaction terms through the electromagnetic tensor Fαβ and the Ricci tensor Rαβ. © E.M. OVSIYUK, 2015.


Ovsiyuk E.M.,Mozyr State Pedagogical University | Kazmerchuk K.V.,Mozyr State Pedagogical University
Nonlinear Phenomena in Complex Systems | Year: 2015

A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit the existence of the non-relativistic limit in the covariant Dirac equation. Procedure for transition to the Pauli approximation is conducted in the equations in the variables (t, r), obtained after separating the angular dependence of (θ, ϕ) from the wave function. The non-relativistic systems of equations in the variables (t, r) is solved exactly in both models. The constructed wave functions do not represent stationary states with fixed energy, however the corresponding probability density does not depend on the time. © 2015, Education and Upbringing Publishing. All rights reserved.


Shepelevich V.V.,Mozyr State Pedagogical University | Makarevich A.V.,Mozyr State Pedagogical University | Shandarov S.M.,Tomsk State University of Control Systems and Radioelectronics
Technical Physics Letters | Year: 2014

We have experimentally studied the dependence of the diffraction efficiency of nonoblique transmission holograms in a (Formula Presented)-cut Bi12TiO20 photorefractive crystal on the orientation angle. For theoretical explanation of the obtained results, it is necessary to assume that the crystal contains amplitude gratings in addition to the phase gratings. © 2014, Pleiades Publishing, Ltd.


Shepelevich V.V.,Mozyr State Pedagogical University
Journal of Applied Spectroscopy | Year: 2011

The evolution of the theoretical and experimental background for a photorefractive effect in cubic gyrotropic piezocrystals is reviewed. It is shown that the impact of the inverse piezoelectric effect and the photoelasticity on the formation and properties of holograms recorded in such crystals is not reduced to minor quantitative variations in their output characteristics but gives rise to qualitative changes both in the orientation and polarization dependences of the hologram diffraction efficiency and in the gain of an object wave at the expense of a reference one. Contributions of various scientific optical schools to the development of theoretical and experimental investigations on the photorefractive effect in cubic piezoelectric crystals are acknowledged and the importance of the experimental results is demonstrated. Particular emphasis is placed on ways to optimize the output characteristics of holograms recorded in cubic gyrotropic photorefractive piezocrystals. Among these are the choice of crystal cut, the selection of the crystal orientation, and the polarization of the light waves. © 2011 Springer Science+Business Media, Inc.


Ovsiyuk E.M.,Mozyr State Pedagogical University
Nonlinear Phenomena in Complex Systems | Year: 2012

It is shown that the generally covariant extended method of Riemann - Silberstein - Majorana - Oppenheime in electrodynamics, specified in Schwarzschild metrics, after separating the variables reduces the problems of electromagnetic solutions to a differential equation similar to that arising in the case of a scalar filed in the Schwarzschild space-time. This differential equation is recognized as a confluent Heun equation. Also, the electromagnetic field is treated on the base of 10-dimensional Duffin - Kemmer approach, when in addition to six components of the strength tensor one uses a 4-component electromagnetic potential. Corresponding system of 10 radial equations is simplified by the use of additional constraints steaming from eigenvalue equation for the spatial parity operator P{cyrillic}Ψ= PΨ; the radial system is divided into two subsystems of 4 and 6 equations respectively. In this second approach the problem of electromagnetic field reduces to the confluent Heun differential equation as well. In particular, we show explicitly how solutions found in complex form are embedded into the 10-dimensional formalism. Besides we determine radial functions that are responsible for gauge degrees of freedom.


Ovsiyuk E.,Mozyr State Pedagogical University
Nonlinear Phenomena in Complex Systems | Year: 2012

In the paper complete systems of exact solutions for Dirac and Weyl equations in the Lobachevsky space H3 are constructed on the base of the method of separation of the variables in quasi-cartesian coordinates. An extended helicity operator is introduced. It is shown that solution constructed when translating to the limit of vanishing curvature coincide with common plane wave solutions on Minkowski space going in opposite z-directions. It is shown the problem posed in Lobachevsky space simulates a situation in the flat space for a quantum-mechanical particle of spin 1/2 in a 2-dimensional potential barrier smoothly rising to infinity on the right.


Shepelevich V.V.,Mozyr State Pedagogical University | Makarevich A.V.,Mozyr State Pedagogical University | Shandarov S.M.,Tomsk State University of Control Systems and Radioelectronics
Physics Procedia | Year: 2015

The results of experimental and theoretical studies of the readout process of the mixed transmission holograms recorded in a photorefractive Bi12TiO20 piezocrystal are presented. It is shown, that in comparison with the case of pure phase holograms, traditionally considered in photorefractive sillenite crystals, additional accounting of the amplitude component of the holographic grating leads to a qualitative and quantitative changes in the diffraction efficiency of holographic gratings recorded in this crystal, which allows to successfully interpreting the experimental results. © 2015 The Authors.

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