Efficient Algorithm forMany-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells

作     者：Christian B.Mendl 

作者机构：Zentrum MathematikTechnische Universitat MunchenBoltzmannstraße 385748 Garching bei MunchenGermany 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2016年第19卷第1期

页      面：192-204页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：The author would like to thank Gero Friesecke for many helpful discussions and DFG for financial support under project FR 1275/3-1 

主　　题：Angular momentum and spin symmetry atomic many-electron quantum systems symbolic computation 

摘      要：We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic *** is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum *** algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.