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A Chebychev propagator for inhomogeneous Schrödinger equations

J. Chem. Phys. 130, 124108 (2009); doi:10.1063/1.3098940

Published 24 March 2009

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Mamadou Ndong,1 Hillel Tal-Ezer,2 Ronnie Kosloff,3 and Christiane P. Koch1
1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
2School of Computer Sciences, The Academic College of Tel-Aviv Yaffo, 2 Rabenu Yeruham St., Tel-Aviv 61803, Israel
3Department of Physical Chemistry and The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
A propagation scheme for time-dependent inhomogeneous Schrödinger equations is presented. Such equations occur in time dependent optimal control theory and in reactive scattering. A formal solution based on a polynomial expansion of the inhomogeneous term is derived. It is subjected to an approximation in terms of Chebychev polynomials. Different variants for the inhomogeneous propagator are demonstrated and applied to two examples from optimal control theory. Convergence behavior and numerical efficiency are analyzed. ©2009 American Institute of Physics
History: Received 23 December 2008; accepted 24 February 2009; published 24 March 2009
Permalink: http://link.aip.org/link/?JCPSA6/130/124108/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 02.30.Yy
    Control theory
  • 02.10.De
    Algebraic structures and number theory
  • 02.30.Hq
    Ordinary differential equations
  • 02.60.Lj
    Ordinary and partial differential equations; boundary value problems
  • YEAR: 2009

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ISSN:
0021-9606 (print)   1089-7690 (online)
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