PROGRAM SUMMARY
Title of program:
PERSYS
Catalogue identifier:
ADPI
Ref. in CPC:
143(2002)83
Distribution format: gzip file
Operating system: MS-DOS, Unix
Number of lines in distributed program, including test data, etc:
907
Keywords:
System of coupled Schrodinger equations, Singular potential,
Regular solution, Piecewise perturbation method, Polynomial and
logarithmic terms, General purpose, Differential equations.
Programming language used: Fortran
Computer:
386/486/Pentium PCs ,
HP Series 9000-715/50UX .
Nature of physical problem:
Problems which involve the integration of the coupled channel
Schrodinger equation and when the singularities of the potential near
the origin causes difficulties. Such problems appear, for example, in
the determination of Gamow states in a deformed potential which are
solutions regular at the origin and, asymptotically, of outgoing wave
form, Ol = Gl + iFl, where Gl and Fl are the irregular and regular
Coulomb wave functions.
Method of solution:
A method based on a perturbative procedure in which the centrifugal term
of the potential, which dominates near the origin, is used to produce
the main part of the solution, while the rest of the potential is seen
as a perturbation from which the solution is improved by successive
iterations. The solutions appear as a sum of purely polynomials or a
combination of polynomial and logarithmic terms. A preliminary step is
required in which the non-singular parts of the potential are fitted by
a parabola.
Typical running time:
The code is usually very fast. The running times depend on the number
of equations (cubically), on how complicated are the expressions of the
potentials and, consequently, on how many operations are required in the
fitting step and on the processor.
References:
[1] L.Gr. Ixaru, Numerical Methods for Differential Equations and
Applications (Reidel, Dordrecht-Boston-Lancaster, 1984) Sec 3.6.