This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator...This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.展开更多
We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped m...We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.展开更多
A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equati...A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.展开更多
We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions t...We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional NikiforovUvarov method. The normalization constant for the Hulthen potential is also computed.展开更多
In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector...In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.展开更多
Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simulta...Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.展开更多
We propose a method for construction of exactly solvable ring-shaped potentials where the linear homogeneous second-order differential equation satisfied by special function is subjected to the extended transformation...We propose a method for construction of exactly solvable ring-shaped potentials where the linear homogeneous second-order differential equation satisfied by special function is subjected to the extended transformation comprising a coordinate transformation and a functional transformation to retrieve the standard Schr?dinger polar angle equation form in non-relativistic quantum mechanics. By invoking plausible ansatze, exactly solvable ring-shaped potentials and corresponding angular wave functions are constructed. The method is illustrated using Jacobi and hypergeometric polynomials and the wave functions for the constructed ring-shaped potentials are normalized.展开更多
Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov...Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.展开更多
We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. ...We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.展开更多
The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the pha...The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.展开更多
文摘This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.
文摘We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.
基金Supported by the National Natural Science Foundation of China under Grant No. 60806047the Basic Research of Chongqing Education Committee under Grant No. KJ060813
文摘A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.
文摘We present the solutions of the Schrodinger equation with the Hulthen potential plus ring-shape potential for l≠ 0 states within the framework of an exponential approximation of the centrifugal potential. Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional NikiforovUvarov method. The normalization constant for the Hulthen potential is also computed.
基金The project supported by the Protessor and Doctor Foundation of Yancheng Teachers College
文摘In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.
基金Supported by National Natural Science Foundation of China under Grant No.10865003
文摘Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.
文摘We propose a method for construction of exactly solvable ring-shaped potentials where the linear homogeneous second-order differential equation satisfied by special function is subjected to the extended transformation comprising a coordinate transformation and a functional transformation to retrieve the standard Schr?dinger polar angle equation form in non-relativistic quantum mechanics. By invoking plausible ansatze, exactly solvable ring-shaped potentials and corresponding angular wave functions are constructed. The method is illustrated using Jacobi and hypergeometric polynomials and the wave functions for the constructed ring-shaped potentials are normalized.
文摘Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.
基金Supported by the National Natural Science Foundation of China under Grant No.11275165partly by 20140772-SIP-IPN,Mexico
文摘We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.
基金Project supported by the National Natural Science Foundation of China(Grant No.11275165)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010291)partly by Secretaria de Investigacio'ny Posgrado de Instituto Polite'cnico Nacional,Mexico(Grant No.20131150-SIP-IPN)
文摘The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.
