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Dynamique quantique par une méthode de paquets d'ondes. Etude des collisions électron-hydrogène et atome-dihydrogène

Abstract : The thesis concerns the development and implementation of numerical
methods for solving the time-dependent Schrödinger equation. We first considered the case of electron-hydrogen scattering. The originality of our method is the use of a non-uniform radial grid defined by a Schwartz interpolation based on a Coulomb reference function. This grid allows many hydrogen bound states and associated matrix elements of various operators to be reproduced to machine accuracy. The wave function is propagated in time using a Split-Operator method. The efficiency of our method allows the wave function to be propagated out to large distances for all partial waves. We obtain excitation and ionisation cross sections in excellent agreement with the best experimental and theoretical data. We subsequently adapted the method and the program package to study reactive atom-dihydrogen scattering. The wave packet is described using product Jacobi coordinates on a regular grid of radial coordinates combined with a basis of Legendre polynomials for the angular part (partial wave S). The wave function is analysed using a time-to-energy Fourier transform, which provides results over the energy range covered by the initial wave packet in one calculation. The method was first tested on the quasi-direct (F,H2) reaction and then applied to the indirect (C(1D),H2)reaction. The state-to-state reaction probabilities are in good agreement with those obtained by a time-independent approach. In particular, the strongly resonant structure of the (C(1D),H2)reaction probabilities is well reproduced.
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Contributor : Liza Mouret <>
Submitted on : Monday, May 19, 2003 - 11:32:05 AM
Last modification on : Tuesday, January 12, 2021 - 4:37:28 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 8:30:42 PM


  • HAL Id : tel-00002842, version 1


Liza Mouret. Dynamique quantique par une méthode de paquets d'ondes. Etude des collisions électron-hydrogène et atome-dihydrogène. Physique Atomique [physics.atom-ph]. Université Rennes 1, 2002. Français. ⟨tel-00002842⟩



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