Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

doi:10.1088/1674-1056/22/10/100302

Abstract The exact solutions of the Schrödinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the “κ/2π scale”, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

Keywords: double ring-shaped Coulomb potential super-universal associated-Legendre polynomial functional analysis method

Received: 17 February 2013
Revised: 10 April 2013
Accepted manuscript online:

PACS:	03.65.Db	(Functional analytical methods)
	03.65.Ge	(Solutions of wave equations: bound states)
	03.65.Nk	(Scattering theory)

Fund: 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 partly by Secretaria de Investigacióny Posgrado de Instituto Politécnico Nacional, Mexico (Grant No. 20131150-SIP-IPN).

Corresponding Authors: Chen Chang-Yuan
E-mail: yctcccy@163.net

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Chen Chang-Yuan (陈昌远), Lu Fa-Lin (陆法林), Sun Dong-Sheng (孙东升), Dong Shi-Hai (董世海) Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics 2013 Chin. Phys. B 22 100302

[1]	Hartmann H 1972 Theor. Chim. Acta 24 201
[2]	Hartmann H, Schuck R and Radtke J 1976 Theor. Chim. Acta 42 1
[3]	Hartmann H and Schuck R 1980 Int. J. Quantum Chem. 18 125
[4]	Sökmen I 1986 Phys. Lett. A 115 249
[5]	Mandal B P 2000 Int. J. Mod. Phys. A 15 1225
[6]	Chetouani L, Guechi L and Hammann T F 1987 Phys. Lett. A 125 277
[7]	Blado G G 1996 Int. J. Quantum Chem. 58 431
[8]	Gerry C C 1986 Phys. Lett. A 118 445
[9]	Chetouani L, Guechi L and Hammann T F 1992 J. Math. Phys. 33 3410
[10]	Vaidya A N and Boschi Filho H B 1990 J. Math. Phys. 31 1951
[11]	Granovskii Y I, Zhedanov A S and Lutzenko I M 1991 J. Phys. A: Math. Gen. 24 3887
[12]	Zhedanov A S 1993 J. Phys. A: Math. Gen. 26 4633
[13]	Chen C Y, Liu C L and Sun D S 2002 Phys. Lett. A 305 341
[14]	Chen C Y, Sun D S and Liu C L 2003 Phys. Lett. A 317 80
[15]	Chen C Y, Lu F L and Sun D S 2004 Phys. Lett. A 329 420
[16]	Yeşiltaş Ö 2008 Chin. Phys. Lett. 25 1172
[17]	Zhang M C 2012 Acta Phys. Sin. 61 240301 (in Chinese)
[18]	Lu F L, Zhuang G C and Chen C Y 2006 J. At. Mol. Phys. 23 493 (in Chinese)
[19]	Hautot A 1973 J. Math. Phys. 14 1320
[20]	Dutra A S and Hott M 2006 Phys. Lett. A 356 215
[21]	Berkdemir C 2009 J. Math. Chem. 46 139
[22]	Lu F L and Chen C Y 2010 Chin. Phys. B 19 100309
[23]	Sun G H and Dong S H 2010 Mod. Phys. Lett. A 25 2849
[24]	Zhang M C and Huangfu G Q 2010 Acta Phys. Sin. 59 6819 (in Chinese)
[25]	Hassanabadi H, Molaee Z and Zarrinkamar S 2012 Mod. Phys. Lett. A 27 1250228
[26]	Bskkeshizadeh S and Vahidi V 2012 Adv. Studies Theor. Phys. 6 733
[27]	Falaye B J 2012 Few-Body Syst. 53 563
[28]	Arda A and Sever R 2012 J. Math. Chem. 50 1484
[29]	Maghsoodi E, Hassanabadi H and Zarrinkamar S 2013 Chin. Phys. B 22 030302
[30]	Chen C Y and Hu S Z 1995 Acta Phys. Sin. 44 9 (in Chinese)
[31]	Gradshteyn I S and Ryzhik I M 2000 Tables of Integrals, Series, and Products, 6th edn. (New York: Academic Press)
[32]	Landau L D and Lifshitz E M 1977 Quantum Mechanics (Non-relativistic Theory), 3rd edn. (New York: Pregamon Press)

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