|
|
|
|
|
|
 |
|
|
CP Methods for the Schrödinger Equation Revisited
|
|
|
|
|
|
|
|
|
|
|
|
| Journal of Computational and Applied Mathematics |
|
|
|
|
|
|
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.
|
|
|
|
|
|
|
|
|
|
|
|
Schrödinger equation, CP methds, initial-value problems, eigenvalue problem, error analysis
|
|
|
|
|
|
|
| | | | | |
|
For the newest resources, visit Wolfram Repositories and Archives »
