A simple O(4,2) approximation of hydrogenic coulomb integrals

✍ Scribed by Carl Wulfman; Sukeyuki Kumei

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 160 KB
• Volume: 23
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(73)85099-7

✦ Synopsis

Repulsion integrals for electrons with hydrogenic wavefunctions are erpresscd in terms ol opcralions of the Lie algebra of the group O(4.2) X 0(4,2). The result is used to obtain approximate expressions for Coulomb integrals as functions ofhydrogenic quantum numbers.

Even in the case of hydrogenic wavefunctions, electron repulsion integrals have a very complex dependence upon the quantum numbers of the functions involved. Indeed, no one has given an explicit formulation of this dependence in the general case, in part perhaps, because the result would be'too complicated to be directly useful. However, it has been recognized recently that the quantum mechanics of an n-particle Coulomb system is formulable in terms of operations of the direct sum ofrz 0(4,2) algebras and the corresponding group, acting upon a denumerable basis [l] . This brings new structure and techniques to bear upon the integrals problem. Using the notation of BednCr [2] the two-electron integral involving hydrogenic functions qOj = 9 ,,~mcl(~,~;ln,) is Y = n,"b"cr~d/(ZaZbZcz~)"2 ; >bj = %?&n,"i) ; F=S -' rS uibk C]dk ' S U-bh = 'a-'b,