The Dirac Equation in the Low Energy Limit

Sammanfattning: The purpose of this work is to give an introduction to relativistic quantum mechanics for the electron. First a review of the Dirac equation and its application to a free electron and an electron in an electromagnetic field will be given. In particular the hydrogen atom is studied. The low energy limit and the lowest order corrections to non-relativistic quantum mechanics are investigated. These corrections include, among others, the gyromagnetic ratio of the electron and spin-orbit coupling in the hydrogen atom. The low energy limit will be studied both in the usual Pauli-Dirac representation and by using the Foldy-Wouthuysen transformation. The Pauli-Dirac representation is used to obtain the correction terms for the energy levels in the hydrogen atom. The Foldy-Wouthuysen transformation is applied to obtain the corresponding Hamiltonian corrections to order α4 .