We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form ...We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail. The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.展开更多
We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider th...We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.展开更多
The pseudospin symmetry （PSS） limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, th...The pseudospin symmetry （PSS） limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, the pseudospin doublets, e.g., 2p3/2 and lf5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative nature of the proposed PSS limits is also discussed.展开更多
We inquire into spin and pseudospin symmetries of the Dirac equation under a Mbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and...We inquire into spin and pseudospin symmetries of the Dirac equation under a Mbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures.展开更多
The concepts of spin and pseudospin symmetries has been used as mere rhetorics to decorate the pseudoscalar potential [Chin. Phys. B 22 090301 （2013）]. It is also pointed out that a more complete analysis of the bou...The concepts of spin and pseudospin symmetries has been used as mere rhetorics to decorate the pseudoscalar potential [Chin. Phys. B 22 090301 （2013）]. It is also pointed out that a more complete analysis of the bound states of fermions in a pseudoscalar Cornell potential has already been published elsewhere.展开更多
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 te...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 Schrtdinger-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.展开更多
Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary ...Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.展开更多
The Cornell potential consists of Coulomb and linear potentials, i.e.-a/r＋br, that it has received a great deal of attention in particle physics. In this paper, we present exact solutions of the Dirac equation with t...The Cornell potential consists of Coulomb and linear potentials, i.e.-a/r＋br, that it has received a great deal of attention in particle physics. In this paper, we present exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits in 3＋1 dimensions. The energy eigenvalues and corresponding eigenfunctions are given in explicit forms.展开更多
Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary q...Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and ~~. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.展开更多
In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum numb...In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.展开更多
A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic ...A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic moment of inertia J varies with ω much faster than the kinematic moment of inertia J, and the ω variation of moments of inertia may be quite different for various SD bands, under certain conditions a near equality of J (hence E_γ) of two 'identical' SD bands may occur in certain frequency range (|δE_γ/E_γ|=|δJ/J|～10^(-3)), and the angular momentum alignments may appear to be approximately quantized. But the situation turns out to be different in other frequency regions. The present phenomenological analysis seems to be consistent with the configuration assignments made by the available microscopic theory in the framework of strong-coupling model. No pseudospin symmetry is involved in the present analysis.展开更多
The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of...The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.展开更多
In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uni...In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate analytical expressions for the energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by using the Nikiforov-Uvarov (NU) method, in closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.展开更多
The ground states of two-component miscible Bose–Einstein condensates（BECs） confined in a rotating annular trap are obtained by using the Thomas–Fermi（TF） approximation method.The ground state density distributi...The ground states of two-component miscible Bose–Einstein condensates（BECs） confined in a rotating annular trap are obtained by using the Thomas–Fermi（TF） approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.展开更多
The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscala...The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The energy eigenvalues and corresponding eigenfunctions are given in closed form.展开更多
文摘We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique. A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail. The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.
文摘We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.
基金Supported by Guizhou Science and Technology Foundation (J[2010]2135)Major State Basic Research Development (973) Program (2007CB815000)+1 种基金NSFC (10975008)China Postdoctoral Science Foundation (20100480149)
文摘The pseudospin symmetry （PSS） limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, the pseudospin doublets, e.g., 2p3/2 and lf5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative nature of the proposed PSS limits is also discussed.
文摘We inquire into spin and pseudospin symmetries of the Dirac equation under a Mbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures.
文摘The concepts of spin and pseudospin symmetries has been used as mere rhetorics to decorate the pseudoscalar potential [Chin. Phys. B 22 090301 （2013）]. It is also pointed out that a more complete analysis of the bound states of fermions in a pseudoscalar Cornell potential has already been published elsewhere.
基金supported by Hibah Peneliti Utama(PUT UNS)2014DIKTI(Grant No.165a/UN27.11/PN2013)
文摘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 Schrtdinger-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.
基金supported by the Scientific and Technological Research Council of Turkey
文摘Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.
文摘The Cornell potential consists of Coulomb and linear potentials, i.e.-a/r＋br, that it has received a great deal of attention in particle physics. In this paper, we present exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits in 3＋1 dimensions. The energy eigenvalues and corresponding eigenfunctions are given in explicit forms.
文摘Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and ~~. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.
文摘In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.
文摘A reliable phenomenological analysis of superdeformed(SD)bands shows that the so-called 'identical' SD bands in general may have different bandhead moments of inertia (δJ_o/J_o≥10^(-2)). Because the dynamic moment of inertia J varies with ω much faster than the kinematic moment of inertia J, and the ω variation of moments of inertia may be quite different for various SD bands, under certain conditions a near equality of J (hence E_γ) of two 'identical' SD bands may occur in certain frequency range (|δE_γ/E_γ|=|δJ/J|～10^(-3)), and the angular momentum alignments may appear to be approximately quantized. But the situation turns out to be different in other frequency regions. The present phenomenological analysis seems to be consistent with the configuration assignments made by the available microscopic theory in the framework of strong-coupling model. No pseudospin symmetry is involved in the present analysis.
基金Project supported by the Scientific and Technical Research Council of Turkey
文摘The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.
文摘In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate analytical expressions for the energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by using the Nikiforov-Uvarov (NU) method, in closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91430109 and 11404198)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111401110004)the Natural Science Foundation of Shanxi Province,China(Grant No.2014011005-3)
文摘The ground states of two-component miscible Bose–Einstein condensates（BECs） confined in a rotating annular trap are obtained by using the Thomas–Fermi（TF） approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.
文摘The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The energy eigenvalues and corresponding eigenfunctions are given in closed form.
