2008/01/21 by Tobias Kramer, Eric J. Heller, Robert E. Parrott · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #cond-mat.mes-hall
paper · pdf · doi:10.1088/1742-6596/99/1/012010
published as J. Phys.: Conference Series, 99, 012010 (2008) [Open Access] · 11 pages, to appear in the Journal of Physics: Conference Series "Time-dependent methods in Quantum Mechanics"
arxiv created 2008/01/21 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 Schrödinger 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.