Hans Bethe, Quantum Mechanics, and the Lamb Shift

An elementary derivation of the Lamb Shift, as originally given by Hans Bethe, is attempted, with a short historical background on the evolution of QED since the beginning of the last century. The treatment is for a non-relativistic electron, in keeping with Bethe's proverbial insight into the problem, which renders irrelevant the effect of the electron spin on the problem. The Kramer idea of renormalization is implemented through a simple subtraction of the self-energy of a free electron from that of the electron bound in a hydrogen atom.