Integrals involved in the perturbation theory of a hydrogen-like system. I

✍ Scribed by J. MŁodzki; A. Lusakowski; M. Suffczyński

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 397 KB
• Volume: 34
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(84)90171-1

✦ Synopsis

Title ofprogram: GREEN are involved in evaluating corrections to the wave function in first order perturbation theory. The formulae for these integrals Catalogue number: ACDH can be expressed in terms of polynomials multiplied by an exponential, an exponential integral and a logarithm [5]. The Program obtainable from: CPC Program Library, Queen's Uni-procedures implementing the algebra of the polynomials over versity of Belfast, N. Ireland (see application form in this issue) rational fractions [2] enable analytical evaluation of these formulae. The matrix elements of the lth partial wave of the n th Computer: CDC 6000; Installation: Computer Centre reduced Coulomb Green's function between functions CYFRONET, Institute of Nuclear Research, Otwock, 05-400 r~exp( -r 2/n) and r1'" exp( -r1/n) are encountered in evaluat-Swierk, Poland ing second order corrections to energy. For 1 < n they are evaluated by next integration of the previously mentioned Operating system: SCOPE 3.4.4 formulae, but when I ~n it was possible to evaluate them by use of another method which is published separately in the Programming language used: PASCAL 6000 [1] following paper [6]. High speed storage required: for compilation: 54000~,for run: Restrictions on the complexity of the program 15700~The numbers n, 1, k, m satisfy the following conditions: n = 1, 2 5, 1 = 0 n, m = 0, 1 8 for one dimensional in-No. of bits ma word: 60 tegrals,andn=1,2 5,/=0 n-1,k,m=0,1 8for matrix elements. No. of lines in combined program and test deck: 1652 Typical running time