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

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.

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

References in corpus (5)

• Coherent Branched Flow in a Two-Dimensional Electron Gas
• Imaging Magnetic Focusing of Coherent Electron Waves
• Matter waves from quantum sources in a force field
• The photoelectric effect in external fields
• Quantum theory of an atom laser originating from a Bose-Einstein condensate or a Fermi gas in the presence of gravity

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• Gate-defined coupled quantum dots in topological insulators
• Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions
• Half integer features in the quantum Hall Effect: experiment and theory
• Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem