Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] acdh_v1_0.gz(16 Kbytes)
Manuscript Title: Integrals involved in the perturbation theory of a hydrogen-like system. I.
Authors: J. Mlodzki, A. Lusakowski, M. Suffczynski
Program title: GREEN
Catalogue identifier: ACDH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 34(1984)199
Programming language: Pascal.
Computer: PDC 6000.
Operating system: SCOPE 3.4.4.
RAM: 15K words
Word size: 60
Keywords: Atomic physics, Wave function, Perturbation theory, Coulomb green's reduced Function, Hydrogen-like system.
Classification: 2.7.

Nature of problem:
Computation of the first order corrections to wave functions and the second order corrections to energy of the nth bound state of a hydrogen-like system.

Solution method:
The definite integrals of the lth partial wave of the nth reduced Coulomb Green's function multiplied by r1m exp(-r1/n) are involved in evaluating corrections to the wave function in first order perturbation theory. The formulae for these integrals can be expressed in terms of polynomials multiplied by an expontential, an expotential integral and a logarithm. The procedures implementing the algebra of the polynomials over rational fractions enable analytical evaluation of these formulae. The matrix elements of the lth partial wave of the nth reduced Coulomb Green's function between functions r2k exp(-r2/n) and r1m exp(-r1/n) are encountered in evaluating second order corrections to energy. For 1<n they are evaluated by next integration of the previously mentioned formulae, but when 1>=n it was possible to evaluate them by use of another method which is published seperately in the following paper.

The numbers n, l, k, m satisfy the following conditions:
n = 1,2..5, 1 = 0..n, m = 0,1..8 for one dimensional integrals, and
n = 1,2..5, 1 = 0..n-1, k,m = 0,1..8 for matrix elements.

Running time:
compilation - 14 s evaluation of one dimensional integral - 150 ms evaluation of matrix element - 30 ms