Solutions Of Dirac Equation Research Articles

Analytical Solution of Dirac Equation for q-Deformed Hyperbolic Manning-Rosen Potential in D Dimensions using SUSY QM and its Thermodynamics'Application

The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.

Quantum Forces in a Relativistic Entangled "Space-Time" State in Complex Hamiltonian Dynamics

Based on complex quantum Hamilton-Jacobi theory and its natural complex spacetime configuration, we realized new states for both positive and negative values of energy and momentum, and we discuss this complex configuration in a relativistic entangled "space-time" state and the resultant 12 extra wave functions than the four solutions of Dirac equation for a free particle. Accordingly, we calculate the quantum forces between particles and antiparticles in a relativistic entangled "space-time" state.

Dirac方程式の厳密解の可視化

Dirac方程式の厳密解の可視化

Relativistic Energy Analysis of Five-Dimensionalq-Deformed Radial Rosen-Morse Potential Combined withq-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separableq-deformed quantum potentials. Theq-deformed hyperbolic Rosen-Morse potential is perturbed byq-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equationlD-1have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum numberncauses the increase of bound state relativistic energy level in both dimensionsD=5andD=3. The bound state relativistic energy level decreases with increasing of both deformation parameterqand orbital quantum numbernl.

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method**Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.

Approximate Solutions of Dirac Equation with Hyperbolic-Type Potential**This research was partially supported by the Scientific and Technical Research Council of Turkey

The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, , by writing in terms of confluent Heun functions. The numerical values of energy are then obtained by fixing the zeros on “E-axis” for both complex functions and .

Observation of Weyl nodes in TaAs

In 1929, H. Weyl proposed that the massless solution of Dirac equation represents a pair of new type particles, the so-called Weyl fermions [1]. However the existence of them in particle physics remains elusive for more than eight decades. Recently, significant advances in both topological insulators and topological semimetals have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon: when two non-degenerate bands in the three-dimensional momentum space cross in the vicinity of Fermi energy (called as Weyl nodes), the low energy excitation behaves exactly the same as Weyl fermions. Here, by performing soft x-ray angle-resolved photoemission spectroscopy measurements which mainly probe bulk band structure, we directly observe the long-sought-after Weyl nodes for the first time in TaAs, whose projected locations on the (001) surface match well to the Fermi arcs, providing undisputable experimental evidence of existence of Weyl fermion quasiparticles in TaAs.

Bound state solutions of Dirac equation with repulsive scalar linear potential

Abstract

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schioberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space-time) states, the original version of EPR paradox can be discussed and the correct answer can be verified based on the strong rooted complex quantum Hamilton-Jacobi theory [2-27] and as another example we can use the negative energy states, to remove the Klein's paradox without the need of any further explanations or justifications like backwardly moving electrons. Finally, comparing the two approaches, we can point out to the existence of a connection between quantum Hamiltonian dynamics, standard quantum field theory, and Krein space quantization [28-43].

Exact Solution of Dirac Equation for q-Deformed Trigonometric Scarf potential with q-Deformed Trigonometric Tensor Coupling Potential for Spin and Pseudospin Symmetries Using Romanovski Polynomial

The bound state solutions of Dirac equation for q-deformed trigonometric Scarf potential with q-deformed trigonometric cotangent and cosecant tensor coupling potential under spin and pseudospin symmetric limits are investigated using Supersymmetric Quantum Mechanics (SUSY QM) method. The new tensor potentials proposed is inspired by superpotential form in SUSY quantum mechanics. The Dirac equations for Scarf potential coupled by new tensor potential in the pseudospin and spin symmetric cases reduce to Schrodinger type equations for shape invariant potential since the proposed new potentials are equivalent to the superpotential of q-deformed trigonometric Scarf potential. The relativistic wave functions are exactly obtained by using SUSY operator method and the relativistic energy equation are exactly obtained by using SUSY method and the idea of shape invariance in the approximation scheme of centrifugal term. The new tensor potential causes the energy degeneracies is omit both for pseudospin and spin symmetric case.

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric (SUSY) quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrödinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.

Approximate solutions of Dirac equation for Tietz and general Manning-Rosen potentials using SUSYQM

In this paper, we consider the relativistic Dirac equation with Tietz and general Manning-Rosen potential. By using appropriate approximation, we obtained the approximate analytical solutions of the Dirac equation for the combined potential via the supersymmetric quantum mechanics (SUSYQM). Within the framework of spin and pseudospin symmetry limits, we obtained the relativistic energy eigenvalus and the corresponding components of the wave functions for Tietz and Manning-Rosen potential using the SUSYQM. We have also reported some numerical results and figures to show the effect of the tensor interactions.

Solution of Dirac Equation with Modified Hylleraas Potential under Spin and Pseudospin Symmetry

Solution of Dirac Equation with Modified Hylleraas Potential under Spin and Pseudospin Symmetry

Solution of Dirac Equations for Cotangent Potential with Coulomb-type Tensor Interaction for Spin and Pseudospin Symmetries Using Romanovski Polynomials

Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Abstract   The bound state solutions of Dirac equations for cotangent function potential with the Coulomb-type tensor potential under spin and pseudospin symmetric limits are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are obtained for spin and pseudospin symmetries exactly. The radial wave functions are obtained in terms of Romanovski polynomials in the limit of spin and pseudospin symmetric conditions. The Coulomb type tensor potential removes the doublet degeneracies for pseudospin and spin symmetric cases. The relativistic energy spectrum for the exact spin symmetric case reduces to the non-relativistic energy spectrum in the non-relativistic limit.     Abstrak   Solusi Persamaan Dirac untuk Potensial K otangen dengan Tensor Interaksi Tipe-Coulomb untuk Simetri Spin dan Pseudospin Menggunakan Polinomial Romanovski. Solusi keadaan terikat dari persamaan Dirac untuk potensial fungsi kotangen dengan potensial tensor tipe-Coulomb untuk simetri spin dan pseudospin diperoleh menggunakan polinomial Romanovski terbatas. Aproksimasi spektrum energi relativistik diperoleh secara eksak untuk simetri spin dan pseudospin. Fungsi gelombang radial diperoleh dalam bentuk polinomial Romanovski untuk keadaan simetri spin dan pseudospin. Potensial tensor tipe-Coulomb menghilangkan degenerasi doublet untuk kedua kasus simetri spin dan pseudospin. Pada batas non-relativistik, spektrum energi relativistik untuk kasus simetri spin eksak tereduksi menjadi spektrum energi non-relativistik.   Keywords: cotangent potential, Coulomb-type tensor, Dirac equation, pseudospin symmetry, Romanovski polynomials /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

Solution of Dirac equation around a charged rotating black hole

The aim of this paper is to solve the radial parts of a Dirac equation in Kerr–Newman (KN) geometry. The potential is replaced by a collection of step functions, then the reflection and transmission coefficients as well as the solution of the wave equation are obtained by using a quantum mechanical method. The result shows that the waves with different values of mass will be scatted off very differently.

Solution of Dirac Equation for q-Deformed Eckart Potential with Yukawa-type Tensor Interaction for Spin and Pseudospin Symmetry Using Romanovski Polynomial

The motion of a nucleon in q-deformed Eckart potential field coupled with Yukawa-type tensor potential is described by using Dirac equation. The bound state solutions of Dirac equation for q-deformed Eckart potential with Yukawa-type tensor potential under exact spin- and pseudospin-symmetric limit are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are exactly obtained within the approximation scheme of centrifugal term. The relativistic energy is negative for pseudospin symmetry and positive for spin symmetry. The radial component of Dirac spinors are obtained in terms of Romanovski polynomials under exact spin- and pseudospin-symmetric conditions. The relativistic energy spectrum for the exact spin-symmetric case reduces to non-relativistic energy spectrum in the non-relativistic limit. Received: 23 October 2013; Revised: 02 November 2013 Accepted: 10 November 2013

Pseudospin and spin symmetry of Dirac equation under Deng–Fan potential and Yukawa potential as a tensor interaction

In this paper, we have presented approximately analytical solution of Dirac equation under the pseudospin and spin symmetry for Deng–Fan potential. We have considered Yukawa potential as a tensor interaction. Some numerical results for energy eigenvalues and the corresponding wave functions of Dirac equation in both pseudospin and spin symmetry are reported. The effect of tensor interaction has been also investigated.

Approximate solutions of Dirac equation with a ring-shaped Woods-Saxon potential by Nikiforov-Uvarov method

An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts of the equation are solved by the Nikiforov-Uvarov method. The general results obtained in this work can be reduced to the standard forms already present in the literature.

Solutions of Dirac Equation with Generalized Rotating Deng-Fan Potential

We present the approximate solution of the Dirac equation with generalized Rotating Deng-Fan potential under spin and pseudospin symmetry limits using a parametric generalized NIkiforov–Uvarov method to obtain the energy eigenvalue and the corresponding eigen functions in closed form. We also discussed the special cases of this potential which is consistent with those found in other literatures.