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[Licence| Download | New Version Template] adqf_v1_0.gz(16 Kbytes)
Manuscript Title: LILIX - a package for the solution of the coupled channel Schrodinger equation.
Authors: L.Gr. Ixaru
Program title: LILIX
Catalogue identifier: ADQF_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 147(2002)834
Programming language: Fortran.
Computer: Pentium-based PCs, HP Series 9000-715/50-UX.
Operating system: MS-DOS, Unix.
Keywords: Coupled channel Schrodinger equation, Initial value problem, CP methods, Variable steps, Regularization, General purpose, Differential equations.
Classification: 4.3.

Nature of problem:
Quantum mechanics problems which involve the solution of the coupled channel Schrodinger equation.

Solution method:
On each step the solution is advanced by a transfer matrix whose components are constructed via the CP implementation of the perturbation series in the diagonalization basis of the local reference potential matrix [1]. Two orders of perturbation are included, plus some extra diagonal corrections. The algorithm allows propagating also the solution of the first derivative of the equation with respect to the momentum k. The order of the method is six and, for one and the same partition, the accuracy is practically energy independent.

Running time:
The running time/step tau by subroutine LIX depends on the processor and on the number of equations n. On a laptop with a Pentium II processor one has tau = 1.9 ms and tau = 9.3 ms for n = 10 and n = 20, respectively. For bigger n, tau increases as n**3. When the solution is advanced for both systems of equations (that is the coupled channel equation and its derivative with respect to k), these times are almost doubled.

References:
[1] L.Gr. Ixaru, J. Comput. Phys. 36 (1980) 182; Numerical Methods for Differential Equations and Applications, Reidel, Dordrecht-Boston- Lancaster, 1986.