ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

MA Zhong-Qi; DAI An-Ying

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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

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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.

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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

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

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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.