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1
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S-Wave Bound- and Resonant States of Two Fermions in Simple Cubic Lattice

100%
Bak M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
808-811
EN
Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated. S-wave pair is considered by means of lattice Green functions (LGF). Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity of using LGF's tabulated values. It is found that the actual peak of scattering cross-section is formed on the lower band boundary in discrepancy with formulae of the theory of scattering in solids.
2
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Approximate Solutions of Schrödinger Equation under Manning-Rosen Potential in Arbitrary Dimension via SUSYQM

100%
Hassanabadi H., Lu L., Zarrinkamar S., Liu G., Rahimov H.
Acta Physica Polonica A
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2012
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vol. 122
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issue 4
650-654
EN
The Schrödinger equation under the Manning-Rosen potential is solved in arbitrary dimension via the quantum mechanical idea of supersymmetry. The Pekeris approximation is used to overcome the inconsistency of the potential with the centrifugal term. Comments on the energy eigenvalue behavior versus dimension are included. The inter-dimensional degeneracy for various orbital quantum number l and dimensions D are studied. The expectation values of some physical parameters are reported via the Feynman-Hellmann theorem.
3
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On Generalized Landau Levels

100%
Krasoń P., Milewski J.
Acta Physica Polonica A
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2017
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vol. 132
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issue 1
94-96
EN
We consider the dispersion of energy levels for both standard and inverted quantum harmonic oscillators in the presence of a uniform electromagnetic field. For this analysis we use a solution of the corresponding eigenproblem in terms of the Kummer functions. We find a complete description of the energy levels for a particle of mass m and electric charge q subject to the action of a harmonic oscillator and simultaneous uniform magnetic and electric fields. We also analyze the effect of spin on energy levels for an electron.
4
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On the Scattering of Neutron in the Magnetic Field οf 180° Bloch Wall

100%
Sazonov S.
Acta Physica Polonica A
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2010
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vol. 117
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issue 3
449-453
EN
The exact solution of the Pauli equation has been derived for neutron wave propagating in magnetized continuum containing the magnetization non-uniformity such as the 180° Bloch wall, whose structure corresponds to the Landau-Lifshitz model. The scattering coefficients with and without neutron spin flip are presented as functions of ratio of neutron energy to the media's magnetic induction value. The possibility of narrow (≲100 Å) domain wall width measurement is discussed by the example of YFe_{11}Ti alloy.
5
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Laguerre Polynomial Solutions of a Class of Initial and Boundary Value Problems Arising in Science and Engineering Fields

100%
Gürbüz B., Sezer M.
Acta Physica Polonica A
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2016
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vol. 130
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issue 1
194-197
EN
In this study, we consider high-order nonlinear ordinary differential equations with the initial and boundary conditions. These kinds of differential equations are essential tools for modelling problems in physics, biology, neurology, engineering, ecology, economy, astrophysics, physiology and so forth. Each of the mentioned problems are described by one of the following equations with the specific physical conditions: Riccati, Duffing, Emden-Fowler, Lane Emden type equations. We seek the approximate solution of these special differential equations by means of a operational matrix technique, called the Laguerre collocation method. The proposed method is based on the Laguerre series expansion and the collocation points. By using the method, the mentioned special differential equations together with conditions are transformed into a matrix form which corresponds to a system of nonlinear algebraic equations with unknown Laguerre coefficients, and thereby the problem is approximately solved in terms of Laguerre polynomials. In addition, some numerical examples are presented to demonstrate the efficiency of the proposed method and the obtained results are compared with the existing results in literature.
6
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Green Function on a Quantum Disk for the Helmholtz Problem

100%
Benali B., Boudjedaa B., Meftah M.
Acta Physica Polonica A
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2013
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vol. 124
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issue 4
636-640
EN
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrödinger equation in two-dimensional space. The system considered in this work is a quantal particle that moves in an axi-symmetric potential. At first, we have assumed that the potential V(r) to be equal to a constant V_0 inside a disk (radius a) and to be equal to zero outside the disk. We have used, to derive the Green function, the continuity of the solution and of its first derivative, at r=a (at the edge). Secondly, we have assumed that the potential V(r) is equal to zero inside the disk and is equal to V_0 outside the disk (the inverted potential). Here, also we have used the continuity of the solution and its derivative to obtain the associate Green function showing the discrete spectra of the Hamiltonian.
7
Content available remote

Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

75%
Cotfas N.
Open Physics
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2004
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vol. 2
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issue 3
456-466
EN
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions.
8
Content available remote

Shape-invariant hypergeometric type operators with application to quantum mechanics

75%
Cotfas N.
Open Physics
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2006
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vol. 4
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issue 3
318-330
EN
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape-invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape-invariant operators. All the shape-invariant operators considered are directly related to Schrödinger-type equations.
9
Content available remote

Lattice Green Functions on a Two-Dimensional Rectangular Lattice with Next-Nearest Neighbor Interaction

75%
Bak M.
Acta Physica Polonica A
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2010
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vol. 118
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issue 2
386-388
EN
The analytic formula for the on-site Green function on the two-dimensional rectangular lattice is shown for arbitrary energy, both within the band (complex Green function) and outside the band (real Green function), expressed by means of elliptic integrals. The recursion formulae enabling calculation of the Green functions on other lattice sites are shown.
10
Content available remote

Romanovski polynomials in selected physics problems

63%
Raposo A., Weber H., Alvarez-Castillo D., Kirchbach M.
Open Physics
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2007
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vol. 5
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issue 3
253-284
EN
We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.
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