Scholarlink

<p>Divergent solutions are ubiquitous with perturbation methods. We utilise continued functions, such as the continued exponential, to converge divergent series in perturbation approaches for energy eigenvalues of helium, the Stark effect and the Zeeman effect on hydrogen. We observe that convergence properties are obtained similar to those of the Padé approximation, which is extensively used in literature. Free parameters are not used, which influence the convergence, and only the first few terms in the perturbation series are implemented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Convergence in divergent series related to perturbation methods using continued exponential and Shanks’ transformations

  • 期刊论文

  • 发表日期：

    2026年1月12日

查看全文
  • Venkat Abhignan

摘要

Divergent solutions are ubiquitous with perturbation methods. We utilise continued functions, such as the continued exponential, to converge divergent series in perturbation approaches for energy eigenvalues of helium, the Stark effect and the Zeeman effect on hydrogen. We observe that convergence properties are obtained similar to those of the Padé approximation, which is extensively used in literature. Free parameters are not used, which influence the convergence, and only the first few terms in the perturbation series are implemented.