The operational wave equation and the Zeeman effect

The object of this paper is to develop the theory of the Zeeman effect from the operational wave equation Wψ ={(p+ec -1 G) A+c -1 (p 0 +e V)i A4 +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 P1 , P2 , P3 ; P0 is the energy operator; A1 , A2 , A3 , A4 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 (Am An +An Am )=0 ifm ≠n , 1 ifm =n .