Born Approximation to a Perturbative Numerical Method for the Solution of the Schrodinger Equation

摘要

A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h exp 4 ), while that for the first order derivative is accurate within O. (Atomindex citation 11:509340)