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

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

2008-01-21

arxiv.org/abs/0801.3171v1

J. Phys.: Conference Series, 99, 012010 (2008) [Open Access]

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, to appear in the Journal of Physics: Conference Series "Time-dependent methods in Quantum Mechanics"

Scientific paper

10.1088/1742-6596/99/1/012010

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.

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