Numerical Computation of Time Independent and Dependent Dirac Equation Using Atomically Balanced Operator and B-Spline Basis

It appears your Web browser is not configured to display PDF files. Download adobe Acrobat or click here to download the PDF file.

Click here to download the PDF file.

Creator: 

Rizq, Hebah

Date: 

2014

Abstract: 

This thesis is devoted to the numerical computation of the time-independent Dirac equation (TIDE) and the time-dependent Dirac equation (TDDE) in the prolate spheroidal coordinates.
Analytical and numerical techniques including Galerkin methods, Min-max principle, and Rayleigh-Ritz methods combined with atomically balanced basis are presented to solve the Dirac equation without spectral pollution.
These numerical methods are used to compute the discrete spectrum of the Dirac operator in two-center Coulomb problems for molecules $\mbox{H}_2^+$ and $\mbox{Th}_2^{179+}$. High order B-spline
basis functions are used to obtain accurate results.
As excepted, the numerical results do not show any spurious state.

Subject: 

Mathematics
Applied Mechanics

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Science: 
M.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Applied Mathematics

Parent Collection: 

Theses and Dissertations

Items in CURVE are protected by copyright, with all rights reserved, unless otherwise indicated. They are made available with permission from the author(s).