The Klein-Gordon Equation and Pionic Atoms

Abstract: This bachelor thesis introduces the Klein-Gordon equation and pionic atoms through a historical review. It discusses properties of the equation and its continuity equation based on a comparison with the Schrödinger equation and its continuity equation. The conclusion that the Klein-Gordon equation is a relativistic extension of the Schrödinger equation for spin-0 particles is drawn. This makes it possible to derive a Klein-Gordon equation and Coulomb potential based model for pionic atoms. The transition energies and the charge density for a pionic atom are derived. The model and a Schrödinger equation model are used to draw conclusions on the differences between regular and pionic atoms. Numerical predictions of the models are compared to experimental data and the accuracy of the models is discussed. Properties of the pionic atom are discussed based on the radial charge density.