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Approximating a wavefunction as an unconstrained sum of Slater determinants

J. Math. Phys. 49, 032107 (2008); doi:10.1063/1.2873123

Published 14 March 2008

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Gregory Beylkin,1 Martin J. Mohlenkamp,2 and Fernando Pérez1
1Department of Applied Mathematics, University of Colorado at Boulder, 256 UCB, Boulder, Colorado 80309-0526, USA
2Department of Mathematics, Ohio University, 321 Morton Hall, Athens, Ohio 45701, USA
The wavefunction for the multiparticle Schrödinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods. ©2008 American Institute of Physics
History: Received 25 July 2007; accepted 25 January 2008; published 14 March 2008
Permalink: http://link.aip.org/link/?JMAPAQ/49/032107/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 03.65.Db
    Functional analytical methods in quantum mechanics
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 02.60.-x
    Numerical approximation and analysis
  • 02.30.Mv
    Approximations and expansions
  • 02.30.Rz
    Integral equations
  • 02.10.Yn
    Matrix theory
  • YEAR: 2008

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0022-2488 (print)   1089-7658 (online)
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