ON THE PROBABILITY INTERPRETATION OF THE BOUND STATE WAVE FUNCTION OF THE MESON

Wang Ming-zhong; Zheng Xi-te; Wang Ke-lin; Xian Ding-chang; Zhang Zheng-gang

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1980, Vol. 4> Issue(4) : 433-439

ON THE PROBABILITY INTERPRETATION OF THE BOUND STATE WAVE FUNCTION OF THE MESON

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Abstract：
The probability interpretation of the bound state meson wave functions is discussed by taking the O- meson wave function solved for the nearly flat bottom potential asan example. On the one hand, given a probability amplitude sense to the three dimen-sional wave function of the meson in the configuration space obtained under the equaltime limit of the four dimensional covariant wave functional solved from the B-S equal-tion, the averaged radius<r²> of the meson can be calculated. On the other hand, theelectromagnetic average radius <r²> is evaluated from the slope at the origin of thespace-like electromagnetic form factor of the meson calculated directly from the fourdimensional B-S wave function. The two averaged values are compared and turn outto be in good coincidence (except for the case of scalar coupling, in which the differenceis about 30%). This shows that though the four dimensional B-S wave function doesnot possess a definite sense of probability amplitude, nevertheless, it might be plausibleto give such a sense to the three dimensional configuration space wave function of themeson obtained from the four dimensional one under the equal time limit.

References

[1]	中国科学院原子能研究所基本粒子理论组,原子能,3(1966),137.[2] 冼鼎昌、郑希特、王明中、汪克林、章正刚,物理学报,27(1978), 94,[3] 王明中、郑希特、冼鼎昌、汪克林、章正刚,高能物理与核物理,1(1977),7.[4] 王明中、郑希特、汪克林、冼鼎昌、章正刚,高能物理与核物理,3(1979),572,[5] D. R. Yennie, M. M. Levy and D. G. Ravenhall, Rev. Mod. Phys., 29 (1957), 144.

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Wang Ming-zhong, Zheng Xi-te, Wang Ke-lin, Xian Ding-chang and Zhang Zheng-gang. ON THE PROBABILITY INTERPRETATION OF THE BOUND STATE WAVE FUNCTION OF THE MESON[J]. Chinese Physics C, 1980, 4(4): 433-439.

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Received: 1979-03-20
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 PROBABILITY INTERPRETATION OF THE BOUND STATE WAVE FUNCTION OF THE MESON

Received Date: 1979-03-20
Accepted Date: 1900-01-01
Available Online: 1980-08-05

Abstract: The probability interpretation of the bound state meson wave functions is discussed by taking the O- meson wave function solved for the nearly flat bottom potential asan example. On the one hand, given a probability amplitude sense to the three dimen-sional wave function of the meson in the configuration space obtained under the equaltime limit of the four dimensional covariant wave functional solved from the B-S equal-tion, the averaged radius<r²> of the meson can be calculated. On the other hand, theelectromagnetic average radius <r²> is evaluated from the slope at the origin of thespace-like electromagnetic form factor of the meson calculated directly from the fourdimensional B-S wave function. The two averaged values are compared and turn outto be in good coincidence (except for the case of scalar coupling, in which the differenceis about 30%). This shows that though the four dimensional B-S wave function doesnot possess a definite sense of probability amplitude, nevertheless, it might be plausibleto give such a sense to the three dimensional configuration space wave function of themeson obtained from the four dimensional one under the equal time limit.