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CP Methods for the Schrödinger Equation Revisited

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

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.

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

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