Note on the space part of anti-symmetric wave functions in the many-electron problem

✍ Scribed by John C. Slater

• Publisher: John Wiley and Sons
• Year: 1970
• Tongue: English
• Weight: 577 KB
• Volume: 4
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560040603

✦ Synopsis

Abstract

It is pointed out that if a many‐electron antisymmetric wave function is expanded as a sum of spin‐product functions, each multiplied by a function of coordinates, the resulting functions of coordinates have many of the same useful features found with the symmetric and antisymmetric functions representing singlet and triplet states in a two‐electron system. For finding the energy, or any function of coordinates only, in the approximation in which spin‐orbit interaction is neglected, one such function of coordinates can be used, the spins being disregarded. Simple procedures allow one to find matrix components of such operators as S^2^ and L . S from the functions of coordinates. These procedures are much easier to visualize than the use of projection operators, the permutation group, or other methods in current use. The general procedures are illustrated by application to the three‐electron problem of the lithium atom, as treated by Lunell, Kaldor, and Harris, and their application to the contact hyperfine structure is pointed out.