The operational wave equation and the Zeeman effect

Abstract

The object of this paper is to develop the theory of the Zeeman effect from the operational wave equation W ψ ={(p+ ec -1 G) A+ c -1 ( p 0 + e V) i A 4 + im 0 c ) ψ = 0, (1.1) V being the electrostatic potential of the nucleus and G the electromagnetic potential of the applied magnetic field. The same notation is employed as in a previous paper,* viz., the components of p are the momenum operators P 1 , P 2 , P 3 ; P 0 is the energy operator; A 1 , A 2 , A 3 , A 4 are wave operators, the first three being treated as the components of a vector A. It has been shown* that the energy levels of hydrogen-like atoms can be determined from the operational wave equation without making any restrictions on the wave operators other than Dirac’s conditions ½ (A m A n +A n A m )=0 if m ≠ n , 1 if m = n .