The Foldy-Wouthuysen Transformation and Relativistic Corrections

Abstract

Beyond the Coulomb potential, there are other potentials for which it is also important to be able to calculate the relativistic corrections. Relativistic corrections become increasingly important for nuclei of high atomic number, and it is exactly these, for which the nuclear diameter is no longer negligible, in which the potential deviates from the 1/r form. The canonical transformation of Foldy and Wouthuysen^l transforms the Dirac equation into two decoupled two-component equations. The equation for the components 1 and 2 becomes identical to the Pauli equation in the nonrelativistic limit; it also contains additional terms that give rise to relativistic corrections. The energies for these components are positive. The equation for the components 3 and 4 describes negative energy states.