ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

MA Zhong-Qi; DAI An-Ying

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1988, Vol. 12> Issue(1) : 42-49

ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

MA Zhong-Qi ^, ,
DAI An-Ying

Institute of High Energy Physics,Academia Sinica,Beijing2 Institute of Industry of Beijing

Abstract
HTML
Reference
Related

PDF

Abstract：
The Hamiltonian of a radial equation is defined on a half-line,and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin.If the wave functions are nonvanishing and convergent at the origin,the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin.In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically.Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed.

References

[1]

M. Reed and B. Simon, Methods of Modern Mathematical Physics-Vol. II: Fourier Analysis, Self-Adjoin-tness, subsect. 10.1 (New York, N.Y., 1975).[2] C. Burnap, H. Brysk and P. F. Zweifel, Nuoao Cimenso, 64B(1981), 407.[3] A. S. Goldhaber, Phys. Rea., DI6(1977), 1815 C.J.Callias, ibid,D16(1977), 3068 .[4] Y. Kazama, C. N. Yang and A. S. Goldhaber, Phys. Rev., D15(1977), 2287.[5] H. J. Lipkin, W. I. Weisberger and M. Peshkin, Ann. Phys. (N. Y.) 53(1969), 203[6] 戴显熹和倪光炯, 高能物理与核物理, 2(1978), 225.[7] H. Yamagishi, Phys. Rev., D27(1983), 2383.[8] E. Witten, Phys.Lett, 86B(1979), 283; F. Wilezek, Phys. Rev. Lett., 48(1982), 1146.[9] T. T. Wu and C. N. Yang, Properties of Matter under Unusual Conditions, Ed. H. Mark and S. Fernbach, 1969 (New York: Interscience) p. 344.[10] T. T. Wu and C. N. Yang, Nucl. Phys.,B107(1976), 365.[11] Y. Kazama and C. N. Yang, Phys. Rev.,D15(1977), 2300.[12] 作者感谢倪光炯、汪荣泰教授在1986年大连会议上有启发性的讨论.[13] G.Hooft, Nucl. Phyr., B79(1974), 276; A. M. Polyakov, JETP Lett, 20(1974), 194.[14] W. J. Marciano and I. J. Muzinich, Phys. Rev. Lett., 50(1983), 1035; Z. Q. Ma, Phys. Rev., D32(1985),2203.[15] M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett., 35(1975), 760[16] T. F. Walsh, P. Weisz and T. T. Wu, Nucl. Phys.,B332(1984), 349.

[1]	HUANG Chun-Qing , LUO Xiang-Qian . New Approach to Monte Carlo Hamiltonian and Tes. Chinese Physics C, 2005, 29(9): 928-932.
[2]	HUANG Chun-Qing , LI Yong-Yao , LUO Xiang-Qian . An Approach to non-S States by Applying Effective Monte Carlo Hamiltonian. Chinese Physics C, 2005, 29(7): 717-720.
[3]	JIANG Jun-Qin , LI Jie-Ming . Calculation of the 0⁺⁺ Glueball Mass for 2+1 Dimensional QCD by Using the Improved Lattice Hamiltonian. Chinese Physics C, 2001, 25(10): 941-944.
[4]	LIU Jin-Ming , LI Jie-Ming , GUO Shuo-Hong . Glueball Mass in Improved SU(3) Lattice Hamiltonian in 2+1 Dimensional. Chinese Physics C, 2001, 25(5): 383-387.
[5]	LI JieMing , JIANG JunQin . Calculation of the Glueball Mass for 2+1 Dimensional SU(2) Lattice Gauge Field Theory by Using the Improved Hamiltonian. Chinese Physics C, 2000, 24(12): 1094-1097.
[6]	JIANG JunQin , LI JieMing . Improved Scheme of the Lattice Hamiltonian in 1+1 Dimensional QCD. Chinese Physics C, 2000, 24(3): 208-212.
[7]	HUANG ChunQing , JIANG JunQin , LUO XiangQian . Monte Carlo Effective Hamiltonian in 1+1 Dimensional Case'. Chinese Physics C, 2000, 24(6): 478-483.
[8]	Jiang Junqin , Luo Xiangqian , Guo Shuohong , Liu Jinming . Calculation of the Vacuum Wave Function in 2+1 Dimensional U(1) Gauge Theory by Using the Improved Lattice Hamiltonian. Chinese Physics C, 1999, 23(12): 1152-1157.
[9]	Jiang Junqin , Luo Xiangqian . Calculation of the Vector Meson Mass in 1+1 Dimensional Lattice QCD by Using the Improved Hamiltonian. Chinese Physics C, 1999, 23(7): 644-649.
[10]	Jiang Junqin . The Calculation of the Fermion Condensates by Using the Improved Hamiltonian. Chinese Physics C, 1998, 22(10): 891-895.
[11]	Hu Jimin , Xu Furong , Zheng Chunkai . Vibrational and Rotational Motions Model of Nucleus(Ⅰ) Cranking Bohr-Mottelson Hamiltonian and Analyses of the Rotational Bands of Even-Even Nuclei. Chinese Physics C, 1996, 20(1): 76-84.
[12]	Wang Qun , Xie Qubing . Effective Hamiltonian for Process e⁺e^－→m(qq)+ng. Chinese Physics C, 1995, 19(9): 791-795.
[13]	DENG Wei-Zhen , YANG Ze-Sen , WANG Yu-Cheng . A Non-Hermitian Approach of Dyson Boson Expansion to Interacting Boson Model. Chinese Physics C, 1993, 17(10): 907-911.
[14]	DENG Wei-Zhen , YANG Ze-Sen . Hermitian Boson Expansion Approach of IBM Toward Cross Shell Excitation. Chinese Physics C, 1992, 16(1): 75-81.
[15]	DI Yao-Min , HA Yi-Ming , FU De-Ji . The Effective Hamiltonian With Continuous Variables Representation in IBM-Ⅱ. Chinese Physics C, 1992, 16(9): 849-856.
[16]	LI Yuan-Jie . RADIAL SOLUTIONS OF THE DIRAC EQUATION IN A LEMAITRE METRIC. Chinese Physics C, 1989, 13(8): 701-705.
[17]	CHENG Tan-Sheng , WU Chong-Shi , ZENG Jin-Yan . PARTICLE-NUMBER-CONSERVING APPROACH FOR TREATING CRANKING HAMILTONIAN. Chinese Physics C, 1988, 12(4): 534-540.
[18]	ZHANG Yue-Zhong . ON THE BOUNDARY CONDITION AND CANONICAL S-WAVE HAMILTIONIAN FOR THE DYON-FERMION SYSTEM——THE SURFACE LAGRANGIAN AND GAUGE INVARIANT CHARGE CURRENT. Chinese Physics C, 1986, 10(1): 15-23.
[19]	WU SHI-SHU . ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL U_αβ=M_αβ（ε_β）. Chinese Physics C, 1979, 3(4): 469-483.
[20]	Wu Shi-shu . ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE. Chinese Physics C, 1978, 2(1): 10-22.

Access

Get Citation

MA Zhong-Qi and DAI An-Ying. ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION[J]. Chinese Physics C, 1988, 12(1): 42-49.

MA Zhong-Qi and DAI An-Ying. ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION[J]. Chinese Physics C, 1988, 12(1): 42-49. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2542)
PDF Downloads(473)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

MA Zhong-Qi ^,
DAI An-Ying

Corresponding author: MA Zhong-Qi,

Institute of High Energy Physics,Academia Sinica,Beijing2 Institute of Industry of Beijing

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1988-02-05

Abstract: The Hamiltonian of a radial equation is defined on a half-line,and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin.If the wave functions are nonvanishing and convergent at the origin,the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin.In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically.Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed.