Programs in Physics & Physical Chemistry
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|Manuscript Title: PERSYS - a program for the solution near the origin of coupled channel Schrodinger equation with singular potential.|
|Authors: M. Rizea|
|Program title: PERSYS|
|Catalogue identifier: ADPI_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 143(2002)83|
|Programming language: Fortran.|
|Computer: 386/486/Pentium PCs, HP Series 9000-715/50UX.|
|Operating system: MS-DOS, Unix.|
|Keywords: System of coupled Schrodinger equations, Singular potential, Regular solution, Piecewise perturbation method, Polynomial and logarithmic terms, General purpose, Differential equations.|
Nature of 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.
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.
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.
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