Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve Bethe-Salpeter (BS) equations exactly without any approximation if the kernel of the BS equations exactly is instantaneous, and take positronium as an example to illustrate the general features of the exact solutions. The key step for the approach is from the BS equations to derive a set of coupled and welldetermined integration equations in linear eigenvalue for the components of the BS wave functions equivalently, which may be solvable numerically under a controlled accuracy, even though there is no analytic solution. For positronium,the exact solutions precisely present corrections to those of the corresponding Schrodinger equation in order v1 (v is the relative velocity) for eigenfunctions, in order v2 for eigenvalues, and the mixing between S and D components in JPC = 1- states etc., quantitatively. Moreover, we also point out that there is a questionable step in some existent derivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, we emphasize that one should take the O(v) corrections emerging in the exact solutions into account accordingly if one is interested in the relativistic corrections for relevant problems to the bound states.

作 者： CHANG Chao-Hsi CHEN Jiao-Kai LI Xue-Qian WANG Guo-Li   作者單位： CHANG Chao-Hsi(CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China;Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China)

CHEN Jiao-Kai(Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China;Graduate School of the Chinese Academy of Sciences, Beijing 100039, China)

LI Xue-Qian(CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China;Department of Physics, Nankai University, Tianjin 300071, China)

WANG Guo-Li(Department of Physics, Nankai University, Tianjin 300071, China;Department of Physics, Fujian Normal University, Fuzhou 350007, China) 

刊 名： 理論物理通訊（英文版）  ISTIC SCI 英文刊名： COMMUNICATIONS IN THEORETICAL PHYSICS  年，卷(期)： 2005 43(1)  分類號(hào)：   關(guān)鍵詞： instantaneous BS equation   exact solutions   positronium   relativistic corrections  

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