The Zeeman effect and spherical harmonics

1. The chief object of the present paper is to present a simple system of equations which are competent to determine the frequencies and intensities of the lines in the standard Zeeman effect. By the standard Zeeman effect is meant the type where the terms are given by Landé’s "g "and “γ” formulæ, and where the multiplicity of the two sets of terms is the same. It will probably be held that the theory of such multiplets has been fairly completely understood for the last two years owing to the works of Sommerfeld, Heisenberg, Landé and Pauli, and the main new contribution of the present work is that, whereas these writers gave formulæ valid only either in weak or strong field (except for doublets, where Heisenberg and Jordan give the value for any strength), here we have complete formulæ from which the intensity of any component in any strength of field can be obtained merely from the solution of rather simple algebraic equations. The proper attack on this problem would undoubtedly be by way of the recent work of Heisenberg on the helium spectrum, and his still more recent work on complex spectra; but this theory is still in the making, so that it has not been practicable to apply it here, and to this extent our results are unverified. Their validity rests firstly on a complete verification of all known facts connected with both weak and strong fields (and intermediate fields for doublets), and also on a conformity with the general features of wave mechanics. The work of Heisenberg and Jordan could readily have been adapted to give all the results of the present paper; but it would have been harder to follow because the matrix methods are not so easy for most readers as are spherical harmonics.