The Zeeman Effect and Stark Effect of Hydrogen in Wave Mechanics; The Force Equation and the Virial Theorem in Wave Mechanics

The Zeeman levels of hydrogenic atoms are determined by a new and simple method, neglecting terms in ${\mathrm{H}}^2$. The frequency of the Larmor precession is $L=L_0(1+\frac{E}{m{c}^2})$. $L_0$ is the frequency of precession obtained by Newtonian mechanics and $E$ the energy of the atom. This agrees with a formula of Pauli obtained by ordinary relativity mechanics. The formulae for the first order Stark effect and for the Paschen-Back effect can be obtained by similar methods.