Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

CP Methods for the Schrödinger Equation Revisited
Authors

L. Gr. Ixaru
H. De Meyer
G. Vanden Berghe
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 1997
Volume: 88
Page range: 289-314
Description

On constructing CPM propagators with an abundant number of terms by Mathematica, we have shown that the CPM[N,Q], where N is the number of polynomial terms by which the potential is approximated in each interval and Q the number of corrections introduced, is a methof of order 2N + 2 at low energies if Q >= Floor[2/3 N] + 1 and of order N at high energies if Q >= 1. We have also proven that in the last case the error damps out as 1/Sqrt[E] for both initial- and bundary-value problems. We have written a program for boundary-value problems which is f order 12, 10 at low and high energies respectively, and have found out that it is far more efficient than the well-established codes SL02F, SLEDGE, and SLEIGN.
Subjects

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Quantum Physics
Keywords

Schrödinger equation, CP methds, initial-value problems, eigenvalue problem, error analysis