The Klein Paradox in Relativistic Quantum Mechanics

Abstract

Klein Paradox was an unexpected result published by Oskar Klein in 1929 He obtained a surprising result by applying the Dirac equation to study the electron scattering off a strong potential Klein assumed that the potential energy of the electron was a high step function potential and found that the transmission coefficient was greater than unity and the reflection coefficient was negative This result cannot be explained within the framework of relativistic quantum mechanics It is known that the paradox can be resolved by considering quantum field theory in which pair production and annihilation of the particles and anti-particles are essential properties 　In this thesis we shall describe the Klein paradox in relativistic quantum mechanics We shall explicitly calculate the solutions of the Schr?dinger equation the Klein-Gordon equation and the Dirac equation of a particle in several potentials which include the step function potential and the potential barrier The calculations of the solutions of the equations with the potentials are given We make no attempt to resolve the paradox by considering quantum field theory

Date of Award	2016 Jan 30
Original language	English
Supervisor	Su-Long Nyeo (Supervisor)