The fixed hypernode method for the solution of the many body Schroedinger equation

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We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and computing the energy of the antisymmetric state from the knowledge of the exact ground state energy for the symmetric state. We made two conjectures: first, that this fixed-hypernode energy is an upper bound to the true fermion energy; second that this bound would necessarily be lower than the ... continued below

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Pederiva, F; Kalos, M H; Reboredo, F; Bressanini, D; Guclu, D; Colletti, L et al. January 24, 2006.

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We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and computing the energy of the antisymmetric state from the knowledge of the exact ground state energy for the symmetric state. We made two conjectures: first, that this fixed-hypernode energy is an upper bound to the true fermion energy; second that this bound would necessarily be lower than the usual fixed-node energy using the same antisymmetric trial function. The first conjecture is true, and is proved in this paper. The second is not, and numerical and analytical counterexamples are given. The question of whether the fixed-hypernode energy can be better than the usual bound remains open.

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PDF-file: 14 pages; size: 0.6 Mbytes

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  • Presented at: Pacifichem 2005, Honolulu, HI, United States, Dec 15 - Dec 20, 2005

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  • Report No.: UCRL-CONF-218419
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 877847
  • Archival Resource Key: ark:/67531/metadc878641

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  • January 24, 2006

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  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 7, 2016, 11:48 a.m.

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Pederiva, F; Kalos, M H; Reboredo, F; Bressanini, D; Guclu, D; Colletti, L et al. The fixed hypernode method for the solution of the many body Schroedinger equation, article, January 24, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc878641/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.