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Title: Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schroedinger equation

Abstract

If the Hamiltonian is time dependent it is common to solve the time-dependent Schroedinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.

Authors:
;  [1]
  1. Departement de chimie, Universite de Montreal, Case postale 6128, succursale Centre-ville, Montreal (Quebec) H3C 3J7 (Canada)
Publication Date:
OSTI Identifier:
20658133
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 121; Journal Issue: 23; Other Information: DOI: 10.1063/1.1814103; (c) 2004 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DISSOCIATION; HAMILTONIANS; HYDROFLUORIC ACID; PHOTON-MOLECULE COLLISIONS; PULSES; RUNGE-KUTTA METHOD; SCHROEDINGER EQUATION; TIME DEPENDENCE

Citation Formats

Tremblay, Jean Christophe, and Carrington, Tucker Jr. Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schroedinger equation. United States: N. p., 2004. Web. doi:10.1063/1.1814103.
Tremblay, Jean Christophe, & Carrington, Tucker Jr. Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schroedinger equation. United States. https://doi.org/10.1063/1.1814103
Tremblay, Jean Christophe, and Carrington, Tucker Jr. 2004. "Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schroedinger equation". United States. https://doi.org/10.1063/1.1814103.
@article{osti_20658133,
title = {Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schroedinger equation},
author = {Tremblay, Jean Christophe and Carrington, Tucker Jr},
abstractNote = {If the Hamiltonian is time dependent it is common to solve the time-dependent Schroedinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.},
doi = {10.1063/1.1814103},
url = {https://www.osti.gov/biblio/20658133}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 23,
volume = 121,
place = {United States},
year = {Wed Dec 15 00:00:00 EST 2004},
month = {Wed Dec 15 00:00:00 EST 2004}
}