Computational investigation of wave packet barrier scattering in the complex plane: Examination of the complex quantum potential utilizing numerical analytic continuation techniques

Abstract

In this study, we utilize numerical analytic continuation (NAC) to compute the complex quantum potential from the complex-extension of wave packets computed on the real-axis. The Cauchy method is utilized due to its robustness and flexibility. The Bohm and complex quantum potentials are compared; both potentials display complicated (but dissimilar) structure on the real-axis. We focus on generating numerically accurate maps of the evolving complex quantum potential for the Eckart barrier scattering problem. Although the complex quantum potential is initially constant, it later develops structures for the reflected wave packet that make it just as complicated as Bohm’s quantum potential, at least on the real-axis.