Further consequences and applications of Special Relativity

Abstract

Abstract Atomic physics is essentially based on Quantum Mechanics. Quantum Mechanics makes essential use of the variables that describe positions and momenta (rather than velocities). The starting point for the determination of atomic energy spectra is the quantum mechanical transcription of the energy conservation equation, which in the ‘non relativistic’ situation is the famous ‘Schrödinger equation’. Schrödinger’s equation is based on the Newtonian relation between energy and momentum of a particle of massm 0, given byE=p 2 /2m 0. In special relativistic mechanics, this relation is replaced by (3.25), which approximates the former for momenta that are small compared tomc, but also implies significant deviations from it for larger momenta. In Quantum Mechanics these deviations give rise to ‘relativistic corrections’ to the ‘non-relativistic’ (i.e. basedon the Schrödinger equation) energy levels. A second’relativistic’ correction stems from the transformation rule (3.26), which predicts a magnetic field in the rest system of the electron that moves in the electric field of the atomic nucleus. This magnetic field interacts with the magnetic moment of the electron, thereby producing extra energy contributions.