On the Hermitian of Hamiltonians of Radial Equations

Ma Zhongqi; Dai Anying

Chinese Physics C> 1988, Vol. 12> Issue(S1) : 27-36

On the Hermitian of Hamiltonians of Radial Equations

Ma Zhongqi ¹ ,
Dai Anying ²

1 Institute of High Energy Physics;
2 Beijing Institute of Technology

Abstract
HTML
Reference
Related

PDF

Abstract：
The Hamiltonian of a radial equation is defined on a half-line, and there is an intimate relation between its hermitian and the boundary conditions 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 to the condition for the vanishing 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 a magnetic monopole field are discussed.

[1]	Ya-Peng Zhao , Rui-Rui Zhang , Han Zhang , Hong-Shi Zong . Chiral phase transition from the Dyson-Schwinger equations in a finite spherical volume. Chinese Physics C, 2019, 43(6): 063101. doi: 10.1088/1674-1137/43/6/063101
[2]	A. H. Farajian , M. Bigdeli , S. Belbasi . LOCV calculation of the equations of state and properties of rapidly rotating neutron stars. Chinese Physics C, 2018, 42(6): 065102. doi: 10.1088/1674-1137/42/6/065102
[3]	Rong Wang , Xu-Rong Chen . Dynamical parton distributions from DGLAP equations with nonlinear corrections. Chinese Physics C, 2017, 41(5): 053103. doi: 10.1088/1674-1137/41/5/053103
[4]	Wen-Jun Chen , Hong Ma , De Yu , Xiao-Hu Zeng . Numerical solution to the Bloch equations: paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field. Chinese Physics C, 2016, 40(8): 088201. doi: 10.1088/1674-1137/40/8/088201
[5]	Lei Yang , Cheng-Jian Lin , Hui-Ming Jia , Xin-Xing Xu , Nan-Ru Ma , Li-Jie Sun , Feng Yang , Huan-Qiao Zhang , Zu-Hua Liu , Dong-Xi Wang . Test of the notch technique for determining the radial sensitivity of the optical model potential. Chinese Physics C, 2016, 40(5): 056201. doi: 10.1088/1674-1137/40/5/056201
[6]	ZHOU Li-Juan , ZHENG Bo , ZHONG Hong-Wei , MA Wei-Xing . Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature. Chinese Physics C, 2015, 39(3): 033101. doi: 10.1088/1674-1137/39/3/033101
[7]	ZHANG Zhou-Li , HE Yuan , ZHANG Bin , LI De-Run , SHI Ai-Min , PAN Gang , DU Xiao-Nan , SUN Lie-Peng . Study of influence of radial matcher section end shape on RFQ cavity frequency. Chinese Physics C, 2014, 38(7): 077007. doi: 10.1088/1674-1137/38/7/077007
[8]	CHENG Xiao-Lei , OUYANG Xiao-Ping , LIU Fang . A digital transmission system for high intensity pulsed radial detection. Chinese Physics C, 2013, 37(1): 016102. doi: 10.1088/1674-1137/37/1/016102
[9]	LI Lin , LI Na , WU Yuan-Fang . Azimuthal distributions of radial momentum and velocity in relativistic heavy ion collisions. Chinese Physics C, 2012, 36(5): 423-428. doi: 10.1088/1674-1137/36/5/007
[10]	CHEN Shao-Na , PING Jia-Lun . Radial excitation states of η and η' in the chiral quark model. Chinese Physics C, 2012, 36(8): 681-690. doi: 10.1088/1674-1137/36/8/001
[11]	XIAO Chen , HE Yuan , YUAN You-Jin , WANG Zhi-Jun , LIU Yong , HE Shou-Bo , XU Meng-Xin , CHANG Wei , LI Chao , YUE Wei-Ming , ZHAO Hong-Wei , XIA Jia-Wen . Numerical optimization and multi-particle dynamics simulation of the radial matching section of the RFQ. Chinese Physics C, 2011, 35(10): 964-968. doi: 10.1088/1674-1137/35/10/015
[12]	ZHANG Yun-Jian , MA Qiao-Sheng , LUO Xiong . Study of a compact external magnetic field radial split-cavity oscillator. Chinese Physics C, 2011, 35(4): 381-386. doi: 10.1088/1674-1137/35/4/011
[13]	WANG Han-Kui , GAO Zao-Chun , CHEN Yong-Shou , GUO Jian-You , CHEN Yong-Jing , TU Ya . The structure of the spherical tensor forces in the USD and GXPF1A shell model Hamiltonians. Chinese Physics C, 2011, 35(8): 753-757. doi: 10.1088/1674-1137/35/8/010
[14]	G. Eichmann , A. Krassnigg , D. Nicmorus . Hadron properties from QCD bound-state equations: A status report. Chinese Physics C, 2010, 34(9): 1175-1180.
[15]	Richard Williams , Christian S . Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation. Chinese Physics C, 2010, 34(9): 1500-1503. doi: 10.1088/1674-1137/34/9/084
[16]	ZHONG Jun-Qing , AN Shi-Zhong , YAO Hong-Juan , ZHANG Tian-Jue , BI Yuan-Jie . Influence of radial magnetic field on emittance in the median plane at CYCIAE-100. Chinese Physics C, 2009, 33(S2): 53-55. doi: 10.1088/1674-1137/33/S2/014
[17]	Zeng Xianghua , Ge Lingxiao . Thermalization,Expansion, and Radial Flow in HIC. Chinese Physics C, 1997, 21(S2): 47-52.
[18]	Deng Weizhen , Yang Zeshen , Wang Yucheng . A Non-Hermitian Approach of Dyson Boson Expansion in Interacting Boson Model. Chinese Physics C, 1993, 17(S3): 285-290.
[19]	Yu Qingchang . The Fluid Theory of Self-Sustaining Magnetically Confined Electron Clouds (I) Fluid Equations. Chinese Physics C, 1991, 15(S1): 17-24.
[20]	MA Zhong-Qi , DAI An-Ying . ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION. Chinese Physics C, 1988, 12(1): 42-49.

Access

Get Citation

Ma Zhongqi and Dai Anying. On the Hermitian of Hamiltonians of Radial Equations[J]. Chinese Physics C, 1988, 12(S1): 27-36.

Ma Zhongqi and Dai Anying. On the Hermitian of Hamiltonians of Radial Equations[J]. Chinese Physics C, 1988, 12(S1): 27-36. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1986-11-05

Article Metric

Article Views(326)
PDF Downloads(4)
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 Hamiltonians of Radial Equations

Ma Zhongqi ^1,
Dai Anying ^2,

1 Institute of High Energy Physics;
2 Beijing Institute of Technology

Received Date: 1986-11-05

Abstract: The Hamiltonian of a radial equation is defined on a half-line, and there is an intimate relation between its hermitian and the boundary conditions 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 to the condition for the vanishing 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 a magnetic monopole field are discussed.