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1
Content available Scattering of massive Dirac particles by a Kink-like potential
100%
Ikot A. , Obong H. P. , Hassanabadi H. , Abbey T. M. , Zarrinkamar S.
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tom 70
EN
The scattering state of spin ½ particles with Kink-like potential is studied under the massive Dirac equation. We obtain the scattering states in terms of the hypergeometric functions and calculate the reflection coefficient (R) and transmission coefficient (T).
2
Content available remote Dirac equation with multiparameter-potential and Hulthén tensor interaction under relativistic symmetries
100%
Ortakaya S.
Open Physics
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2014
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tom 12
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nr 12
822-829
EN
The pseudospin and spin symmetric solutions of the Dirac equation with Hulthén-type tensor interaction are obtained under multi-parameter-exponential potential (MEP) for arbitrary κ states. The energy eigenvalues and the corresponding eigenfunctions are also obtained using the parametric Nikiforov-Uvarov (NU) method. Some numerical results are also obtained for pseudospin and spin symmetry limits.
3
Content available remote Bound state of solution of Dirac-Coulomb problem with spatially dependent mass
100%
Olğar E. , Dhahir H. , Mutaf H.
Open Physics
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2014
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tom 12
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nr 4
292-296
EN
The bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.
4
Content available remote De Sitter spacetime as a momentum measuring apparatus
100%
Nicolaevici N.
Open Physics
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2012
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tom 10
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nr 1
51-60
EN
We discuss the evolution of a quantum wave packet in the expanding de Sitter spacetime using the plane wave solutions of the Dirac equation. We concentrate on the case of large negative times when the packet approaches the event horizon and confirm that the evolution accords with that expected from the classical trajectories. We point out that in certain conditions the packet can split into two components that become localized at different parts of the horizon and that this effect can be seen, in an idealized sense, as a measuring process for the momentum of the particle, in direct analogy with the measurement of spin in a Stern-Gerlach experiment.
5
Content available remote Pseudospin symmetry and a double ring-shaped spherical harmonic oscillator potential
100%
Zhang M.-C.
Open Physics
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2009
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tom 7
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nr 4
768-773
EN
A new double ring-shaped spherical harmonic oscillator potential is presented. The pseudospin symmetry in this system is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained and some particular cases are discussed.
6
Content available remote Transmission resonance for a Dirac particle in a one-dimensional Hulthén potential
100%
Guo J. , Yu Y. , Jin S.
Open Physics
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2009
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tom 7
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nr 1
168-174
EN
We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.
7
Content available remote Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any κ-value
100%
Arda A. , Sever R. , Tezcan C.
Open Physics
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2010
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tom 8
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nr 5
843-849
EN
The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
8
Content available remote The hypergeneralized Heun equation in quantum field theory in curved space-times
100%
Batic D. , Sandoval M.
Open Physics
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2010
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tom 8
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nr 3
490-497
EN
We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.
9
Content available remote Solution of the Dirac equation with magnetic monopole and pseudoscalar potentials
88%
Aghaei S. , Chenaghlou A.
Open Physics
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2014
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tom 12
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nr 4
266-273
EN
The Dirac equation in the presence of the Dirac magnetic monopole potential, the Aharonov-Bohm potential, a Coulomb potential and a pseudo-scalar potential, is solved by separation of variables using the spinweighted spherical harmonics. The energy spectrum and the form of the spinor functions are obtained. It is shown that the number j in spin-weighted spherical harmonics must be greater than $$\left| q \right| - \tfrac{1} {2}$$.
10
Content available remote Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
88%
Ikhdair S. , Sever R.
Open Physics
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2010
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tom 8
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nr 4
652-666
EN
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = $$ \tilde l $$ = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.
11
Content available remote Approximate κ-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry
75%
Ikhdair S.
Open Physics
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2012
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tom 10
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nr 2
361-381
EN
Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.
12
Content available On the Complementary Wave Interpretation of the Dirac Equation
75%
Bulathsinghala D. L. , Wijewardena Gamalath K. A. I. L.
International Letters of Chemistry, Physics and Astronomy
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2013
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tom Vol. 9, iss. 2
103-115
EN
The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.
13
Content available remote Implementation of a quantized line element in Klein-Gordon and Dirac fields
63%
Bulathsinghala D. L. , Wijewardena Gamalath K. A. I. L.
International Letters of Chemistry, Physics and Astronomy
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2015
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tom Vol. 48
68--86
EN
In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the timeenergy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.
14
Content available remote An introduction to the edition of two Lemaître’s original manuscripts
51%
Maere C. d. , Lambert D.
Demonstratio Mathematica
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2017
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tom Vol. 50, nr 1
2--27
EN
The aim of this paper is to explain the contributions of G. Lemaître to Spinor Theory. At the end of the paper, we edited also, for the first time two short manuscripts: Spineurs et Quanta and Les spineurs et la physique quantique, written by Lemaître in December 1955 and in January 1956. This edition is a way of honouring Professor Michael Heller because he was the first, with Professor Odon Godart, who discovered, classified and published unedited manuscripts of G. Lemaître.
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