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
In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energ...In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.展开更多
By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associa...By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated twocomponent spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case a →0.展开更多
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 th...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.展开更多
We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><...We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><i><i><sub><span style="font-family:Verdana;">n</span></sub></i><span style="font-family:Verdana;"></span></i>, and the momentum eigenstates for the space-like Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.展开更多
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation t...We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number <em>l</em> and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.展开更多
The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quan...The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials and or the generalized hypergeometric functions have been obtained. A short-cut of the Nikiforov-Uvarov (NU) method is used in the solution. A unified treatment of the Eckart, Rosen-Morse, Hulthén and Woods-Saxon potential models can be easily derived from our general solution. The present calculations are found to be identical with those ones appearing in the literature. Further, based on the PT-symmetry, the bound state solutions of the trigonometric Rosen-Morse potential can be easily obtained.展开更多
Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculati...Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.展开更多
The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning–Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa fo...The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning–Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning–Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.展开更多
By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials...By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials for any quantum numbers n and l. Energy eigenvalues and the scattering amplitude are calculated. Some special cases of the problem are also investigated.展开更多
The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the ...The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.展开更多
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.
文摘In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.
文摘By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated twocomponent spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case a →0.
基金supported by the Higher Education Project(Grant No.698/UN27.11/PN/2015)
文摘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.
文摘We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><i><i><sub><span style="font-family:Verdana;">n</span></sub></i><span style="font-family:Verdana;"></span></i>, and the momentum eigenstates for the space-like Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.
文摘We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number <em>l</em> and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.
文摘The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials and or the generalized hypergeometric functions have been obtained. A short-cut of the Nikiforov-Uvarov (NU) method is used in the solution. A unified treatment of the Eckart, Rosen-Morse, Hulthén and Woods-Saxon potential models can be easily derived from our general solution. The present calculations are found to be identical with those ones appearing in the literature. Further, based on the PT-symmetry, the bound state solutions of the trigonometric Rosen-Morse potential can be easily obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.11405128Natural Science Basic Research Plan in Shaanxi Province of China under Grant No.15JK2093
文摘Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.
文摘The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning–Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning–Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.
文摘By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials for any quantum numbers n and l. Energy eigenvalues and the scattering amplitude are calculated. Some special cases of the problem are also investigated.
文摘The relativistic problem of spin-1/2 fermions subject to vector hyperbolic （kink-like） potential （- tanh kx） is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials in two cases.
