Meshless basis set for solving one-dimensional time independent Schrodinger Equation

The ability of Schrödinger equation in representing the energies and wave function of the molecular system has attracted many scientists to find the best solution for it. Due to the restriction of this equation that can only be solved analytically for the simple molecular models; numerous of numeric...

Full description

Saved in:

Bibliographic Details
Main Author:	Teh, Huey Ching
Format:	Thesis
Language:	English
Published:	2011
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/47960/25/TehHueyChingMFS2011.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.47960
record_format	uketd_dc
spelling	my-utm-ep.479602018-05-30T03:39:37Z Meshless basis set for solving one-dimensional time independent Schrodinger Equation 2011-06 Teh, Huey Ching QA Mathematics The ability of Schrödinger equation in representing the energies and wave function of the molecular system has attracted many scientists to find the best solution for it. Due to the restriction of this equation that can only be solved analytically for the simple molecular models; numerous of numerical methods were introduced to solve it. The Fourier grid Hamiltonian (FGH) method introduced by Marston and Balint-Kurti in 1989 solved the one-dimensional time independent Schrödinger equation for H2 molecule by using the plane wave basis set and coupling with the Fast Fourier Transform (FFT) technique to reduce the computational time. In this study, we implement the Meshless Element Free Galerkin (MEFG) method to solve the same problem. The localized basis sets adopted in this method and the compactness properties of the weight function lead us to generate a sparse Hamiltonian matrix in finding the eigenvalues and eigenfunctions. The aim of this study is to develop a new numerical approach to solve the one-dimensional time independent Schrödinger equation and as a preliminary research work for us to investigating into the computational quantum mechanics studies. 2011-06 Thesis http://eprints.utm.my/id/eprint/47960/ http://eprints.utm.my/id/eprint/47960/25/TehHueyChingMFS2011.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Teh, Huey Ching Meshless basis set for solving one-dimensional time independent Schrodinger Equation
description	The ability of Schrödinger equation in representing the energies and wave function of the molecular system has attracted many scientists to find the best solution for it. Due to the restriction of this equation that can only be solved analytically for the simple molecular models; numerous of numerical methods were introduced to solve it. The Fourier grid Hamiltonian (FGH) method introduced by Marston and Balint-Kurti in 1989 solved the one-dimensional time independent Schrödinger equation for H2 molecule by using the plane wave basis set and coupling with the Fast Fourier Transform (FFT) technique to reduce the computational time. In this study, we implement the Meshless Element Free Galerkin (MEFG) method to solve the same problem. The localized basis sets adopted in this method and the compactness properties of the weight function lead us to generate a sparse Hamiltonian matrix in finding the eigenvalues and eigenfunctions. The aim of this study is to develop a new numerical approach to solve the one-dimensional time independent Schrödinger equation and as a preliminary research work for us to investigating into the computational quantum mechanics studies.
format	Thesis
qualification_level	Master's degree
author	Teh, Huey Ching
author_facet	Teh, Huey Ching
author_sort	Teh, Huey Ching
title	Meshless basis set for solving one-dimensional time independent Schrodinger Equation
title_short	Meshless basis set for solving one-dimensional time independent Schrodinger Equation
title_full	Meshless basis set for solving one-dimensional time independent Schrodinger Equation
title_fullStr	Meshless basis set for solving one-dimensional time independent Schrodinger Equation
title_full_unstemmed	Meshless basis set for solving one-dimensional time independent Schrodinger Equation
title_sort	meshless basis set for solving one-dimensional time independent schrodinger equation
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2011
url	http://eprints.utm.my/id/eprint/47960/25/TehHueyChingMFS2011.pdf
_version_	1747817273586876416

Meshless basis set for solving one-dimensional time independent Schrodinger Equation

Similar Items