环状非有心球谐振子势场赝自旋对称性的三对角化表示

张民仓

doi:10.7498/aps.61.240301

摘要

提出一个包含非有心电耦极矩势的环状谐振子模型, 在能够负载波动算子三对角化矩阵表示的完全平方可积L2空间讨论了这一势场的赝自旋对称性. 利用三对角化矩阵方案, 给出了波函数角向分量和径向分量展开系数满足的三项递推关系式. 角向波函数和径向波函数分别以Jacobi 多项式和Laguerre多项式表示, 由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱. 并以Descartes多项式的符号法则讨论了能量方程的代数结构.

关键词:

Abstract

A noncentral harmonic oscillatory ring-shaped potential is proposed, in which the noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relations for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound state is obtained by diagonalizing the radial recursion relation. The algebraic property of energy equation is also discussed, showing the exact pseudospin symmetry

Keywords:

作者及机构信息

张民仓

1.
陕西师范大学物理学与信息技术学院, 西安 710062

Authors and contacts

Zhang Min-Cang

1.
College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

参考文献

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[2]	Hecht K T, Adler A 1969 Nucl. Phys. A 137 129
[3]	Ginocchio J N 1999 Phys. Rep. 315 231
[4]	Dudek J, Nazarewicz W, Szymanski Z, Leander G A 1987 Phys. Rev. Lett. 59 1405
[5]	Nazarewicz W, Twin P J, Fallon P, Garrett J D 1990 Phys. Rev. Lett. 64 1654
[6]	Zeng J Y, Meng J, Wu C S, Zhao E G, Xing Z, Chen X Q 1991 Phys. Rev. C 44 R1745
[7]	Schiff L I 1955 Quantum mechanics 3rd ed. (McGraw-Hill, New York)
[8]	Mayer M G 1950 Phys. Rev. 78 16
[9]	Nilsson S G 1955 Dan. Mat. Fys. Medd. 29 16
[10]	Chen T S, Lu H F, Meng J 2003 Chin.Phys. Lett. 20 358
[11]	Kukulin V I, Loyola G, Moshinsky M 1991 Phys. Lett. A 158 19
[12]	Ginocchio J N 2004 Phys. Rev. C 69 034318
[13]	Quesne C 1988 J. Phys. A: Math. Gen. 21 3093
[14]	Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378
[15]	Berkdemir C, Cheng Y F 2009 Phys. Scr. 79 1
[16]	Lisboa R, Malheiro M, de Castro A S, Alberto P , Fiolhais M 2004 Phys. Rev. C 69 024319
[17]	Fermi E, Teller E 1947 Phys. Rev. 72 399
[18]	Wightman A S 1950 Phys. Rev. 77 521
[19]	Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[20]	Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[21]	Coon S A, Holstein B R 2002 Am. J. Phys. 70 513
[22]	Jaramillo B, Núñez-Yépez H N, Salas-Brito A L 2010 Phys. Lett. A 374 2707
[23]	Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[24]	Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 374 841
[25]	Alhaidari A D 2008 Ann. Phys. 323 1709
[26]	Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[27]	Alhaidari A D 2007J. Phys. A: Math. Theor. 40 14843
[28]	Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[29]	Bahlouli H, Abdelmonem M S, Nasser I M 2010 Phys. Scr. 82 065005
[30]	Alhaidari A D 2005 Ann. Phys. 317 152
[31]	Zeng J Y 2000 Quantum Mechanics Vol Ⅱ 3rd (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷Ⅱ) 第三版(北京: 科学出版社)]
[32]	Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303

施引文献

[1]	Arima A, Harvey M, Shimizu K 1969 Phys. Lett. B 30 517
[2]	Hecht K T, Adler A 1969 Nucl. Phys. A 137 129
[3]	Ginocchio J N 1999 Phys. Rep. 315 231
[4]	Dudek J, Nazarewicz W, Szymanski Z, Leander G A 1987 Phys. Rev. Lett. 59 1405
[5]	Nazarewicz W, Twin P J, Fallon P, Garrett J D 1990 Phys. Rev. Lett. 64 1654
[6]	Zeng J Y, Meng J, Wu C S, Zhao E G, Xing Z, Chen X Q 1991 Phys. Rev. C 44 R1745
[7]	Schiff L I 1955 Quantum mechanics 3rd ed. (McGraw-Hill, New York)
[8]	Mayer M G 1950 Phys. Rev. 78 16
[9]	Nilsson S G 1955 Dan. Mat. Fys. Medd. 29 16
[10]	Chen T S, Lu H F, Meng J 2003 Chin.Phys. Lett. 20 358
[11]	Kukulin V I, Loyola G, Moshinsky M 1991 Phys. Lett. A 158 19
[12]	Ginocchio J N 2004 Phys. Rev. C 69 034318
[13]	Quesne C 1988 J. Phys. A: Math. Gen. 21 3093
[14]	Guo J Y, Han J C, Wang R D 2006 Phys. Lett. A 353 378
[15]	Berkdemir C, Cheng Y F 2009 Phys. Scr. 79 1
[16]	Lisboa R, Malheiro M, de Castro A S, Alberto P , Fiolhais M 2004 Phys. Rev. C 69 024319
[17]	Fermi E, Teller E 1947 Phys. Rev. 72 399
[18]	Wightman A S 1950 Phys. Rev. 77 521
[19]	Fox K, Turner J E 1966 J. Chem. Phys. 45 1142
[20]	Brown W B, Robers R E 1967 J. Chem. Phys. 46 2006
[21]	Coon S A, Holstein B R 2002 Am. J. Phys. 70 513
[22]	Jaramillo B, Núñez-Yépez H N, Salas-Brito A L 2010 Phys. Lett. A 374 2707
[23]	Alhaidari A D 2005 J. Phys. A: Math. Gen. 38 3409
[24]	Zhang M C, Huang-Fu G Q 2012 Ann. Phys. 374 841
[25]	Alhaidari A D 2008 Ann. Phys. 323 1709
[26]	Alhaidari A D, Bahlouli H 2008 Phys. Rev. Lett. 100 110401
[27]	Alhaidari A D 2007J. Phys. A: Math. Theor. 40 14843
[28]	Bahlouli H, Alhaidari A D 2010 Phys. Scr. 81 025008
[29]	Bahlouli H, Abdelmonem M S, Nasser I M 2010 Phys. Scr. 82 065005
[30]	Alhaidari A D 2005 Ann. Phys. 317 152
[31]	Zeng J Y 2000 Quantum Mechanics Vol Ⅱ 3rd (Beijing: Science Press) (in Chinese) [曾谨言 2000 量子力学 (卷Ⅱ) 第三版(北京: 科学出版社)]
[32]	Ginocchio J N, Leviatan A, Meng J, Zhou S G 2004 Phys. Rev. C 69 034303

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