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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.
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关键词:
- 双环形Hulthn势 /
- 任意分波 /
- 近似解析解 /
- 束缚态
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
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[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]
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[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 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 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
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[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 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 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
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