Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations
<p>In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infin...
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California State University, Long Beach
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ndltd-PROQUEST-oai-pqdtoai.proquest.com-15977382015-10-02T03:56:52Z Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations Brown, Natalie Mathematics|Quantum physics|Physics <p>In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy. California State University, Long Beach 2015-10-01 00:00:00.0 thesis http://pqdtopen.proquest.com/#viewpdf?dispub=1597738 EN |
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EN |
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Mathematics|Quantum physics|Physics |
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Mathematics|Quantum physics|Physics Brown, Natalie Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
description |
<p>In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy. |
author |
Brown, Natalie |
author_facet |
Brown, Natalie |
author_sort |
Brown, Natalie |
title |
Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
title_short |
Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
title_full |
Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
title_fullStr |
Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
title_full_unstemmed |
Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations |
title_sort |
matrix continued fraction approach to the relativistic quantum mechanical spin-zero feshbach-villars equations |
publisher |
California State University, Long Beach |
publishDate |
2015 |
url |
http://pqdtopen.proquest.com/#viewpdf?dispub=1597738 |
work_keys_str_mv |
AT brownnatalie matrixcontinuedfractionapproachtotherelativisticquantummechanicalspinzerofeshbachvillarsequations |
_version_ |
1716825580052152320 |