Document Type

Theses, Ph.D

Rights

Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence

Disciplines

1.1 MATHEMATICS

Publication Details

Sucessfully submitted for the award of Doctor of Philosophy to the Technological University Dublin, May, 2009.

Abstract

A covariant formalism of Relativistic Quantum Mechanics is demonstrated, through it's de- velopment and application. The Relativistic Case is shown to follow a similar structure to the established Non-Relativistic formalism. Reasons for preferring the new covariant formalism over the established method are presented. Solutions to the case of a scalar particle in a one-dimensional field are presented. The Relativistic Energy Eigenfunction is derived. Results are generated from initial Gaussian states via a Green's Function method. A Green's Function for the system is derived and applied. The solution to the Quantum System is shown to follow a scaled version of the classical path. The equivalent system in the Non-Relativistic case is also analysed. The Energy Eigenfunc- tion for the time-independent Schrodinger Equation is derived. A Green's Function is derived for the time-dependent SchrÄdinger Equation and solutions to the system are found using intial Gaussian States. A short demonstration of the established method, that of the Klein-Gordon equation, is provided. Some deficiencies in the Klein-Gordon equation are shown. These deficiencies are shown to not exist in the covariant formalism.

DOI

https://doi.org/10.21427/D7QW2F

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