








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 bundaryvalue problems. We have written a program for boundaryvalue 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 wellestablished codes SL02F, SLEDGE, and SLEIGN.












Schrödinger equation, CP methds, initialvalue problems, eigenvalue problem, error analysis







   
 
