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Orbital HP-clouds for quantum systems. (English) Zbl 1158.81326
Ferreira, A. J. M. (ed.) et al., Progress on meshless methods. Invited papers based on the presentations at the 2nd ECCOMAS thematic conference on meshless methods, Porto, Portugal, July 9–11, 2007. Dordrecht: Springer (ISBN 978-1-4020-8820-9/hbk). Computational Methods in Applied Sciences (Springer) 11, 159-173 (2009).
Summary: Solving Schrödinger 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. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schrödinger 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 Schrödinger equation. Analysis of hydrogen systems and a spherical quantum dot demonstrates the effectiveness of the proposed method.
For the entire collection see [Zbl 1151.65003].
MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-08 Computational methods for problems pertaining to quantum theory
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