Orbital HP-clouds for quantum systems

Jiun Shyan Chen; Wei Hu

doi:10.1007/978-1-4020-8821-6_10

Orbital HP-clouds for quantum systems

Jiun Shyan Chen
, Wei Hu

Department of Civil Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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.

Original language	English
Title of host publication	Progress on Meshless Methods
Editors	Ferreira Ferreira, E.J. Kansa, G.E. Fasshauer, V.M.A. Leitão
Publisher	Springer
Pages	159-173
Number of pages	15
ISBN (Print)	9781402088209
DOIs	https://doi.org/10.1007/978-1-4020-8821-6_10
Publication status	Published - 2009
Event	2nd ECCOMAS Thematic Conference on Meshless Methods, 2007 - Porto, Portugal Duration: 2007 Jul 9 → 2007 Jul 11

Publication series

Name	Computational Methods in Applied Sciences
Volume	11
ISSN (Print)	1871-3033

Conference

Conference	2nd ECCOMAS Thematic Conference on Meshless Methods, 2007
Country/Territory	Portugal
City	Porto
Period	07-07-09 → 07-07-11

All Science Journal Classification (ASJC) codes

Civil and Structural Engineering
Modelling and Simulation
Biomedical Engineering
Computer Science Applications
Fluid Flow and Transfer Processes
Computational Mathematics
Electrical and Electronic Engineering

Access to Document

10.1007/978-1-4020-8821-6_10

Cite this

@inproceedings{94c6ca68bf274d39a3452cf4eeefee7d,

title = "Orbital HP-clouds for quantum systems",

abstract = "Solving Schr{\"o}dinger 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 Schr{\"o}dinger 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 Schr{\"o}dinger equation. Analysis of hydrogen systems and a spherical quantum dot demonstrates the effectiveness of the proposed method.",

author = "Chen, \{Jiun Shyan\} and Wei Hu",

note = "Publisher Copyright: {\textcopyright} Springer Science + Business Media B.V. 2009.; 2nd ECCOMAS Thematic Conference on Meshless Methods, 2007 ; Conference date: 09-07-2007 Through 11-07-2007",

year = "2009",

doi = "10.1007/978-1-4020-8821-6\_10",

language = "English",

isbn = "9781402088209",

series = "Computational Methods in Applied Sciences",

publisher = "Springer",

pages = "159--173",

editor = "Ferreira Ferreira and E.J. Kansa and G.E. Fasshauer and V.M.A. Leit{\~a}o",

booktitle = "Progress on Meshless Methods",

}

TY - GEN

T1 - Orbital HP-clouds for quantum systems

AU - Chen, Jiun Shyan

AU - Hu, Wei

N1 - Publisher Copyright: © Springer Science + Business Media B.V. 2009.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84962909466

UR - https://www.scopus.com/pages/publications/84962909466#tab=citedBy

U2 - 10.1007/978-1-4020-8821-6_10

DO - 10.1007/978-1-4020-8821-6_10

M3 - Conference contribution

AN - SCOPUS:84962909466

SN - 9781402088209

T3 - Computational Methods in Applied Sciences

SP - 159

EP - 173

BT - Progress on Meshless Methods

A2 - Ferreira, Ferreira

A2 - Kansa, E.J.

A2 - Fasshauer, G.E.

A2 - Leitão, V.M.A.

PB - Springer

T2 - 2nd ECCOMAS Thematic Conference on Meshless Methods, 2007

Y2 - 9 July 2007 through 11 July 2007

ER -

Orbital HP-clouds for quantum systems

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this