Photon Wave Functions and the Exact Electromagnetic Matrix Elements for Hydrogenic Atoms

Abstract

After reviewing the properties of the photon considered as a quantized particle of zero mass, positive energy, and unit spin, the expansion of the unquantized and quantized electromagnetic fields and vector and scalar potentials in terms of the photon wave functions and creation and destruction operators is reviewed and extended. The most general vector and scalar potentials are obtained through the use of the eigenfunctions of the curl operator. The dichotomy between the photon and wave picture of electromagnetic radiation is discussed and resolved. The results are applied to the calculation of the exact electromagnetic matrix elements and transition probabilities (i.e., with retardation taken into account exactly) for hydrogenic atoms. The exact matrix elements are very simple in form. The notion of multipole radiation of the usual treatments is irrelevant. However, it is shown how multipoles appear as an approximation.