Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics

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Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density ... continued below

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Chen, J; Hu, W & Puso, M October 19, 2006.

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Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schroedinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.

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PDF-file: 29 pages; size: 0.5 Mbytes

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  • Journal Name: Computational Methods in Applied Mechanics, vol. 196, no. 37-40, March 19, 2007, pp. 3693-3705; Journal Volume: 196; Journal Issue: 37-40

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  • Report No.: UCRL-JRNL-225453
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 940145
  • Archival Resource Key: ark:/67531/metadc899535

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  • October 19, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 6, 2016, 3:02 p.m.

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Chen, J; Hu, W & Puso, M. Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics, article, October 19, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc899535/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.