In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for 0 and r coordinates. Exact bound state solutions of Klein-Gordon equation with equal double ring-sha...In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for 0 and r coordinates. Exact bound state solutions of Klein-Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.展开更多
Pschl-Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Pschl-Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC...Pschl-Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Pschl-Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in ψ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrdinger equation with PTDRSC potential are presented. The normalized ψ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.展开更多
文摘In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for 0 and r coordinates. Exact bound state solutions of Klein-Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.
基金Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 05KJD140252)the Natural Science Foundation of Jiangsu Province of China (Grant No. KB2008199)
文摘Pschl-Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Pschl-Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in ψ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrdinger equation with PTDRSC potential are presented. The normalized ψ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.
