Computational investigation of wave packet scattering in the complex plane: Numerical analytic continuation techniques

Abstract

AbstractIn this study, we utilize Numerical Analytic Continuation (NAC) techniques to compute the complex‐extension of wave packets computed on the real‐axis. Various methods for doing this are reviewed, and the accuracy and stability of one particular method (the Cauchy Method) are examined using a test function. We focus on generating numerically accurate maps of the complex‐extended time‐dependent wave packet for the Gaussian and Eckart barrier scattering problems. We also examine quantum momentum function vector fields and the associated Pólya vector fields for this problem. In a companion study, we present a novel method for solving the complex‐extended Schrödinger equation for points in the complex plane for wave packet scattering from a Gaussian barrier. Several fascinating features of the solution (such as quantized vortices) were presented, but we could only check the veracity of those results on the real‐axis. The method utilized in this study provides an additional check of these results. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011