{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-algorithm-for-many-electron-angular","title":"Efficient algorithm for many-electron angular momentum and spin diagonalization on atomic subshells","arxiv_id":"1409.6860","date":"2014-09-24","proceeding":null,"authors":["Christian B. Mendl"],"abstract":"We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensor product $\\wedge^n V_u$, where $n$ is the number of electrons and $u = \\mathrm{s}, \\mathrm{p}, \\mathrm{d},\\dots$ denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is also an $\\boldsymbol{L}^2$ eigenstate (equivalently for $S_z$ and $\\boldsymbol{S}^2$), as well as the traversal of LS eigenstates using the lowering operators $L_-$ and $S_-$. Iterative application to the remaining states in $\\wedge^n V_u$ leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed $n$ and increasing subshell number $u$ yields run time $\\mathcal{O}(u^{3n-2})$. A symbolic computer algebra implementation is available online.","url_abs":"https://arxiv.org/abs/1409.6860v2","url_pdf":"https://arxiv.org/pdf/1409.6860v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-algorithm-for-many-electron-angular","repo_url":"https://github.com/cmendl/irredLS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}