The Research Of Completeness Of Hydrogen Atoms’ State After Adding External Potential

In the study of atomic structures, such as many-body perturbation calculation, requires a large number of intermediate state (virtual wave function). On the other hand, the completeness and effectiveness of the bases obtained with different methods also should be verified. In this paper, the approximately complete basis function series are built using contracted state by adding external potential. We systematically investigate the problem of the completeness of the contracted state basis in hydrogen because the TRK sum rule and Kramers theorem for hydrogen system have the strict theoretical results. The calculation results show that, by selecting rational external potential and the corresponding various step sizes, we can get reasonable calculation accuracy. And we also examine some rules and phenomena in the calculation, as well as effects of adding external potential areas on the calculation results and efficiency, and gives an ideal position to add the external potential.