Separation of different wave components in the Bethe–Salpeter wave function

Pramana

Jiao-Kai Chen1¹ 

[1] Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000, People’s Republic of China$$

关键词: Salpeter wave function;    mixing;    spherical coordinate system;    pure 𝐿 = 𝐽 + 1 term.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by 𝐿 -𝑆 coupling analysis. The cancelation formula is given, by which the terms with pure 𝐿 = 𝐽 + 1 wave components in the Salpeter wave function for the bound state with 𝜂𝑝 = (-1)𝐽 can be obtained by separating the 𝐿 = 𝐽 - 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of 𝐿 = 𝐽 - 1 and 𝐽 + 1 wave states, and for solving the Salpeter equation exactly without approximation.

【 授权许可】

Unknown