Universiti Teknologi Malaysia Institutional Repository

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

Teh, Huey Ching (2011) Meshless basis set for solving one-dimensional time independent Schrodinger Equation. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

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Abstract

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.

Item Type:Thesis (Masters)
Additional Information:Thesis (Sarjana Sains (Matematik)) - Universiti Teknologi Malaysia, 2011; Supervisor : Dr. Yeak Su Hoe
Uncontrolled Keywords:schrodinger equation, The Fourier grid Hamiltonian, preliminary research
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:47960
Deposited By: Narimah Nawil
Deposited On:06 Oct 2015 15:55
Last Modified:30 May 2018 11:39

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