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Analytical Solutions for a Double ring-shaped Noncentral Potential in D-dimensions
Jie Gao,Min-Cang Zhang 한국물리학회 2016 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.69 No.7
In the present study, a generalized double ring-shaped Coulomb noncentral potential is proposed, and the D-dimensional Schr¨odinger equation with this potential is examined in hyperspherical coordinates. The Nikiforov-Uvarov (N-U) method is applied to obtain the D-dimensional energy eigenvalues and the corresponding eigenfunctions. The angular/radial wavefunction is written in terms of Jacobi/Laguerre polynomials.
Solutions of a Generalized Anharmonic Oscillatory Noncentral Potential in Higher Spatial Dimensions
Ya Bai,Min-Cang ZHANG 한국물리학회 2017 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.71 No.5
A generalized anharmonic oscillatory noncentral potential is presented and the D-dimensional Schr¨odinger equation for this noncentral potential is examined in hyperspherical coordinates. The Nikiforov-Uvarov (N-U) method is applied to obtain the D-dimensional energy eigenvalues and the corresponding eigenfunctions. The angular/radial wavefunction is expressed in terms of Jacobi/ Laguerre polynomials. Some special cases of this potential model including the Quesne potential and the ring-shaped non-spherical harmonic oscillatory (RNHO) potential are discussed also.
Chun-Long XU,Min-Cang ZHANG 한국물리학회 2017 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.70 No.2
The arbitrary l-wave solutions to the Schr¨odinger equation for the deformed hyperbolic Manning- Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich’s approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.