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| Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential | |
| 引用本文： | 陆法林,陈昌远. Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential[J]. 中国物理 B, 2010, 19(10): 100309-100309. DOI: 10.1088/1674-1056/19/10/100309 |
| 作者姓名： | 陆法林 陈昌远 |
| 作者单位： | School of Physics Science and Electronic Technology, Yancheng Teachers College, Yancheng 224002, China |
| 基金项目： | Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 05KJD140252) and the Natural Science Foundation of Jiangsu Province of China (Grant No. KB2008199). |
| 摘 要： | Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, 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. |
| 关 键 词： | Pschl–Teller double-ring-shaped Coulomb potential supersymmetry and shape invariance Schrdinger equation bound states |
| 收稿时间： | 2009-07-15 |
Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential |
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| Lu Fa-Lin and Chen Chang-Yuan. Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential[J]. Chinese Physics B, 2010, 19(10): 100309-100309. DOI: 10.1088/1674-1056/19/10/100309 | |
| Authors: | Lu Fa-Lin and Chen Chang-Yuan |
| Affiliation: | School of Physics Science and Electronic Technology, Yancheng Teachers College, Yancheng 224002, China |
| Abstract: | Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, 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. |
| Keywords: | Põ schl--Teller double-ring-shaped Coulomb potential supersymmetry and shape invariance Schrõ dinger equation bound states |
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