Here I provide collected notes that have accumulated over the years of my study of physics. For some rather difficult topics it has helped my understanding to write down everything I know. Also sometimes I got distracted by some phenomenon or topic from the original study, which then dwindles into a really involved calculation. In these cases I also start writing down the steps to keep track.

I think that other students of physics might encounter similar difficulties or questions and so my notes might help them. Over time I will upload more notes once I brought them into a form so that (hopefully) others can read them.

The Quantum Theory of the Hydrogen Atom

This text has started out with my interest in the hydrogenic solution of the Dirac equation. Once I had dealt with it I found that it would be very interesting to make a comparison between the different approaches of quantum theory on the hydrogen atom. Up to date this text presents the application of Heisenberg's matrix mechanics, Schrödinger's and Dirac's theory and Feynman's path integral approach to the hydrogen atom. The application of quantum field theory to calculate radiative corrections to the energy levels is also discussed. This text already contains a lot of information but it will be further extended in the future.

Two uncommon examples of the relativistic motion of an accelerated point particle

In this script I introduce two small yet uncommon examples on the motion of an accelerated point particle in the special theory of relativity: First, the motion in an oscillating potential, -E sin(ωx⁰), and second, the problem of the relativistic harmonic oscillator. The aim of this script is threefold: First, illustrate the Lagrangian and Hamiltonian formalism for the relativistic mechanics of a point particle by means of two simple problems. Second, give a counter-example against the sometimes encountered belief that accelerated motion could not be handled by the special theory of relativity. Third, calculate the time-dilation of the twin-paradox in an example problem with steady motion and velocity.