Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Sinica

Approximate analytical solutions of bound states for the double ring-shaped Hulthn potential

Fa‐Lin Lu, Chen Chang-Yuan, Yuan You

Published Jan 1, 2013• 3 citations
Publisher

Abstract

摘要 构造了双环形Hulthn势, 用指数函数近似表示任意分波的离心项, 运用函数分析法讨论双环型Hulthn势Schrdinger方程的束缚态解. 归一化的角向波函数和径向波函数用超几何多项式表示, 给出了束缚态能谱, 体系的束缚态的能谱方程和波函数与量子数和势参数有关. 中心势场和单环形势场角向波函数及 Hulthn势束缚态能谱是本文双环形Hulthn势的特例. 关键词: 双环形Hulthn势 / 任意分波 / 近似解析解 / 束缚态 Abstract The double ring-shaped Hulthn potential is proposed in this paper. By using the analytical method of function, the approximate analytical solutions of bound state solutions of Schrdinger equation for the double ring-shaped Hulthn potential are presented within the framework of an exponential approximation of the centrifugal potential for arbitrary l-states. The normalized angular and radial wave function expressed in terms of hypergeometric polynomials are presented. The energy spectrum equations are obtained. The wave function and the energy spectrum equations of the system are related to three quantum numbers and parameters of double ring-shaped Hulthn potential. The polar angular wave functions of the central potential and ring-shaped potential and the energy spectrum equations of Hulthn potential turn out to be the special cases of the double ring-shaped Hulthn potential. Keywords: double ring-shaped Hulthn potential / arbitrary l-wave / approximate analytical solution / bound states 作者及机构信息 陆法林, 陈昌远, 尤源 1. 盐城师范学院物理科学与电子技术学院, 盐城 224051 基金项目: 国家自然科学基金(批准号: 11275165)、江苏省自然科学基金(批准号: BK2010291)和盐城师范学院教授博士基金(批准号: 11YSYJB0206)资助的课题. Authors and contacts Lu Fa-Lin, Chen Chang-Yuan, You Yuan 1. School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051, China Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11275165), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010291), and the Professor and Doctor Foundation of Yancheng Teachers University, China (Grant No. 11YSYJB0206). 参考文献 [1] Quesne C 1988 J. Phys. A: Math. Gen. 21 3093 [2] Chen C Y, Sun D S 2001 Acta Photon. Sin. 30 104 (in Chinese) [陈昌远, 孙东升2001光子学报 30 104] [3] Dong S H, Sun G H, Lozada-Cassou M 2004 Phys. Lett. A 328 299 [4] Hartmann H, Schuch D 1980 Int. J. Quantum Chem. 18 125 [5] Chen C Y, Liu C L, Sun D S 2002 Phys. Lett. A 305 341 [6] Zhou F, Wu Y, Guo J Y 2009 Commun. Theor. Phys. 52 813 [7] Chen C Y, Liu C L, Lu F L 2010 Phys. Lett. A 374 1346 [8] Hautot A 1973 J. Math. Phys. 14 1320 [9] Dutra A S, Hott M 2006 Phys. Lett. A 356 215 [10] Yasuk F, Durmus A. 2008 Phys. Scr. 77 015005 [11] Lu F L, Chen C Y 2010 Chin. Phys. B 19 100309 [12] Zhang M C, Huangfu G Q 2010 Acta Phys. Sin. 59 6819 (in Chinese) [张民仓, 皇甫国庆2010物理学报 59 6819] [13] Berkdemir C 2009 J. Math. Chem. 46 139 [14] Zhang M C, Sun G H, Dong S H 2010 Phys. Lett. A 374 704 [15] Ghoumaid A, Benamira F, Guechi L, Khiat Z 2013 Cent. Eur. J. Phys. 11 78 [16] Arda A, Sever R 2012 J. Math. Chem. 50 1484 [17] Maghsoodi E, Hassanabadi H, Zarrinkamar S 2013 Chin. Phys. B 22 030302 [18] Guo J Y, Meng J, Xu F X 2003 Chin. Phys. Lett. 20 602 [19] Zhang M C 2008 Chin. Phys. B 17 3214 [20] Chen C Y, Sun D S, Lu F L 2008 J. At. Mol. Phys. 25 393 (in Chinese) [陈昌远, 孙东升, 陆法林2008 原子与分子物理学报 25 393] [21] Qiang W C, Chen W L, Li K, Zhang H P 2009 Int. J. Mod. Phys. A 24 5523 [22] Feng J S, Liu Z, Guo J Y 2010 Chin. Phys. Lett. 27 110304 [23] Zhang M C, HuangFu G Q 2011 Chin. Phys. Lett. 28 50304 [24] Agboola D 2011 Commun. Theor. Phys. 55 972 [25] Liu S K, Liu S D 2002 Special Function (Beijing: China Meteorological Press) p8, 485, 571, 585 (in Chinese) [刘式适, 刘式达 2002 特殊函数(北京: 气象出版社) 第8, 485, 571, 585页] [26] Gradsgteyn I S, Ryzhik M 2007 Tables of Integrals, Series, and Products (7th Ed.) (New York: Academic Press) p971 [27] Chen C Y, Lu F L, Sun D S, Dong S H 2013 Chin. Phys. B 22 100302 施引文献

DOI
10.7498/aps.62.200301

Related papers

Bound state solution of the Klein–Fock–Gordon equation with the Hulthén plus a ring-shaped-like potential within SUSY quantum mechanics

A. I. Ahmadov, Sh. M. Nagiyev, Mafkura Gojayeva +2 more

In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

arXiv:1812.11179•International Journal of Modern Physics A•Nov 30, 2018•31 citations

Schrödinger Equation with Hulthén Potential Plus Ring-Shaped Potential

D. Agboola

We present the solutions of the Schrödinger equation with the Hulthén 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 Nikiforov—Uvarov method. The normalization constant for the Hulthén potential is also computed.

arXiv:0811.4441•Communications in Theoretical Physics•Jun 1, 2011•34 citations

Bound States Solution of Dirac Equation and Schrdinger Equation for a New Ring Potential

HU Xian-quan

Under strong coupling conditions,the non-relativistic motion of particles and spin zero or half-integer the nature of relativistic particles in the system with the Schrdinger equation and Dirac equation can respectively describe.A new ring-shaped harmonic oscillator potential is proposed in this paper.The exact bound solution of Dirac equation and Schrdinger equation for the above potential is obtained under the condition of equal scalar potentials and vector potentials.They can be separated into an corresponding to the wave function equations of angular and radial wave function equation with the method of separation variables.The normalized angle wave function and radial wave function were expressed respectively in terms of the generalized associated-Legendre function and the confluent hyper-geometric function are presented,that the normalized radial wave function,and then by the radial bound state wave function are satisfied with the boundary conditions,obtains the exact bound state energy spectrum equations.The exact energy spectrum equations are obtained and meanwhile,proper discussion and some important conclusions are presented.

Chongqing Shifan Daxue xuebao. Ziran kexue ban•Jan 1, 2011•0 citations

Bound states of Klein-Gordon equation for ring-shaped non-spherical harmonic oscillator potentials

Fa‐Lin Lu, Chen Chang-Yuan, 盐城师范学院物理系，盐城 224002

By using the ordinary method of variable separation,the bound states of Klein-Gordon equation of the ring-shaped non-spherical harmonic oscillator with equal scalar and vector potentials are solved. The normalized angular wave function expressed in terms of the universal associatedLegendre polynomial and the normalized radial wave function expressed in terms of the confluent hyper-geometric function are presented. The exact energy spectrum equations are obtained.

Acta Physica Sinica•Jan 1, 2004•4 citations

Exact Solutions of Bound States of the Schrdinger Equation with the Ring-Shaped Hartmann Potential

Zidong Chen

The Schrdinger equation with the ring-shaped Hartmann potential is solved by using the usual method of variable separation in spherical polar coordinates. The exact energy equation is obtained by then solved angle equation and radial equation. The normalized angle wavefunction and radial wavefunction are presented. The general calculation formulas for radial matrix elements and radial average values of the Hartmann potential are obtained.

Journal of Southwest China Normal University•Jan 1, 2005•0 citations

The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

H. I. Ahmadov, M. V. Qocayeva, N. Sh. Huseynova

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

International Journal of Modern Physics E•May 1, 2017•20 citations
摘要 构造了双环形Hulthn势, 用指数函数近似表示任意分波的离心项, 运用函数分析法讨论双环型Hulthn势Schrdinger方程的束缚态解. 归一化的角向波函数和径向波函数用超几何多项式表示, 给出了束缚态能谱, 体系的束缚态的能谱方程和波函数与量子数和势参数有关. 中心势场和单环形势场角向波函数及 Hulthn势束缚态能谱是本文双环形Hulthn势的特例. 关键词: 双环形Hulthn势 / 任意分波 / 近似解析解 / 束缚态 Abstract The double ring-shaped Hulthn potential is proposed in this paper. By using the analytical method of function, the approximate analytical solutions of bound state solutions of Schrdinger equation for the double ring-shaped Hulthn potential are presented within the framework of an exponential approximation of the centrifugal potential for arbitrary l-states. The normalized angular and radial wave function expressed in terms of hypergeometric polynomials are presented. The energy spectrum equations are obtained. The wave function and the energy spectrum equations of the system are related to three quantum numbers and parameters of double ring-shaped Hulthn potential. The polar angular wave functions of the central potential and ring-shaped potential and the energy spectrum equations of Hulthn potential turn out to be the special cases of the double ring-shaped Hulthn potential. Keywords: double ring-shaped Hulthn potential / arbitrary l-wave / approximate analytical solution / bound states 作者及机构信息 陆法林, 陈昌远, 尤源 1. 盐城师范学院物理科学与电子技术学院, 盐城 224051 基金项目: 国家自然科学基金(批准号: 11275165)、江苏省自然科学基金(批准号: BK2010291)和盐城师范学院教授博士基金(批准号: 11YSYJB0206)资助的课题. Authors and contacts Lu Fa-Lin, Chen Chang-Yuan, You Yuan 1. School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051, China Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11275165), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010291), and the Professor and Doctor Foundation of Yancheng Teachers University, China (Grant No. 11YSYJB0206). 参考文献 [1] Quesne C 1988 J. Phys. A: Math. Gen. 21 3093 [2] Chen C Y, Sun D S 2001 Acta Photon. Sin. 30 104 (in Chinese) [陈昌远, 孙东升2001光子学报 30 104] [3] Dong S H, Sun G H, Lozada-Cassou M 2004 Phys. Lett. A 328 299 [4] Hartmann H, Schuch D 1980 Int. J. Quantum Chem. 18 125 [5] Chen C Y, Liu C L, Sun D S 2002 Phys. Lett. A 305 341 [6] Zhou F, Wu Y, Guo J Y 2009 Commun. Theor. Phys. 52 813 [7] Chen C Y, Liu C L, Lu F L 2010 Phys. Lett. A 374 1346 [8] Hautot A 1973 J. Math. Phys. 14 1320 [9] Dutra A S, Hott M 2006 Phys. Lett. A 356 215 [10] Yasuk F, Durmus A. 2008 Phys. Scr. 77 015005 [11] Lu F L, Chen C Y 2010 Chin. Phys. B 19 100309 [12] Zhang M C, Huangfu G Q 2010 Acta Phys. Sin. 59 6819 (in Chinese) [张民仓, 皇甫国庆2010物理学报 59 6819] [13] Berkdemir C 2009 J. Math. Chem. 46 139 [14] Zhang M C, Sun G H, Dong S H 2010 Phys. Lett. A 374 704 [15] Ghoumaid A, Benamira F, Guechi L, Khiat Z 2013 Cent. Eur. J. Phys. 11 78 [16] Arda A, Sever R 2012 J. Math. Chem. 50 1484 [17] Maghsoodi E, Hassanabadi H, Zarrinkamar S 2013 Chin. Phys. B 22 030302 [18] Guo J Y, Meng J, Xu F X 2003 Chin. Phys. Lett. 20 602 [19] Zhang M C 2008 Chin. Phys. B 17 3214 [20] Chen C Y, Sun D S, Lu F L 2008 J. At. Mol. Phys. 25 393 (in Chinese) [陈昌远, 孙东升, 陆法林2008 原子与分子物理学报 25 393] [21] Qiang W C, Chen W L, Li K, Zhang H P 2009 Int. J. Mod. Phys. A 24 5523 [22] Feng J S, Liu Z, Guo J Y 2010 Chin. Phys. Lett. 27 110304 [23] Zhang M C, HuangFu G Q 2011 Chin. Phys. Lett. 28 50304 [24] Agboola D 2011 Commun. Theor. Phys. 55 972 [25] Liu S K, Liu S D 2002 Special Function (Beijing: China Meteorological Press) p8, 485, 571, 585 (in Chinese) [刘式适, 刘式达 2002 特殊函数(北京: 气象出版社) 第8, 485, 571, 585页] [26] Gradsgteyn I S, Ryzhik M 2007 Tables of Integrals, Series, and Products (7th Ed.) (New York: Academic Press) p971 [27] Chen C Y, Lu F L, Sun D S, Dong S H 2013 Chin. Phys. B 22 100302 施引文献
In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
Under strong coupling conditions,the non-relativistic motion of particles and spin zero or half-integer the nature of relativistic particles in the system with the Schrdinger equation and Dirac equation can respectively describe.A new ring-shaped harmonic oscillator potential is proposed in this paper.The exact bound solution of Dirac equation and Schrdinger equation for the above potential is obtained under the condition of equal scalar potentials and vector potentials.They can be separated into an corresponding to the wave function equations of angular and radial wave function equation with the method of separation variables.The normalized angle wave function and radial wave function were expressed respectively in terms of the generalized associated-Legendre function and the confluent hyper-geometric function are presented,that the normalized radial wave function,and then by the radial bound state wave function are satisfied with the boundary conditions,obtains the exact bound state energy spectrum equations.The exact energy spectrum equations are obtained and meanwhile,proper discussion and some important conclusions are presented.
In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.