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

Journal Article · Wed Dec 15 00:00:00 EST 2004 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.1814103· OSTI ID:20658133

Tremblay, Jean Christophe; Carrington, Tucker Jr ^[1]

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1. Departement de chimie, Universite de Montreal, Case postale 6128, succursale Centre-ville, Montreal (Quebec) H3C 3J7 (Canada)

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.

• OSTI ID: 20658133
• Journal Information: Journal of Chemical Physics, Vol. 121, Issue 23; Other Information: DOI: 10.1063/1.1814103; (c) 2004 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

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