The Dynamics of Klein-Gordon Equation for a Slow Varying Interacting Wave Field

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
The main purpose of the study was to investigate the outcomes when an interacting term is incorporated into a Klein-Gordon equation, in particular when the interacting term involves a slow periodic wave field. The study further seeks to investigate in the context of Dirac approach to the quantum relativistic free particle. A slow varying periodic field was considered in the study as a potential field which interacted with quantum mechanics wave particle field as in the Schrodinger equation for a forced particle. In the relativistic context of the study, the Klein-Gordon equation was considered as a homogenous differential equation which represented a free particle and the interacting term was placed on the right hand side, having a “slow varying potential” field as a factor. It was found that for the zeroth order approximation of the slow varying wave field, Klein-Gordon equation still remained as field but there was only a shift in the energy mass. However, with the second order approximation, a formal Quantum Harmonic Oscillator was obtained. This yielded discrete positive and negative energy mass, suggesting particle and antiparticle states. An equivalent Dirac formalism which also incorporated an interacting term was obtained, with a recovery of particle and antiparticle states by means of creation and annihilation operators.
A thesis submitted to the Department of Mathematics , Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of the Degree of Master of Philosophy