An efficient and accurate method to obtain the energy-dependent Green function for general potentials

TL;DR

This paper introduces a novel time-dependent approach that efficiently and accurately constructs the energy-dependent Green function for complex potentials, enabling applications across various physics fields.

Contribution

The paper presents a new method to directly obtain the energy-dependent Green function from time-dependent quantum mechanics without ensemble averaging or specific lead-in setups.

Findings

Accurately constructs Green functions for general potentials

Applicable to chemical, mesoscopic, and atomic physics

Outperforms existing methods in flexibility and efficiency

Abstract

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results and a variety of numerical methods have been developed to solve the time-dependent Schroedinger equation. The time-dependent methods work for nearly arbitrarily shaped potentials, including sources and sinks via complex-valued potentials. Many quantities are measured at fixed energy, which is seemingly not well suited for a time-dependent formulation. Very few methods exist to obtain the energy-dependent Green function for complicated potentials without resorting to ensemble averages or using certain lead-in arrangements. Here, we demonstrate in detail a time-dependent approach, which can accurately and effectively construct the energy-dependent Green function for very general potentials. The applications of the method are numerous, including chemical, mesoscopic, and atomic physics.