Wave Theory of the Spin Electron

The matrices are so chosen that they are subject to the same commutation rules as the ordinary components of angular momentum ( 5, p. 127) further, in this case the 2 -direction is the specially distinguished direction, in which the spin, represented by the fourth coordinate, has set itself. For is a diagonal matrix with the proper values (diagonal elements) +1, —1 the 2 -component of the angular momentum has therefore one of the fixed values +1 or —-1. On the other hand, and Sy are not diagonal matrices their values are therefore not measurable simultaneously with but are only statistically determinate. 

If now a magnetic field exists parallel to the -axis, then, by 2 (p. 144), the magnetic energy of the setting of the spin with respect to the field direction is given by 

The factor 2 here arises from the anomaly in the relation between magnetic and mechanical moment in the spin, as compared with the similar relation in the orbit—an anomaly mentioned on p. 142, and explained by Thomas as a consequence of the theory of relativity. In this equation s is the operator of the total spin moment, and cS s cos(,9, H) is its component in the direction of the field. 

As for tlie wave equation itself, in tlie absence of magnetic fields it runs exactly like tbe Scbrodinger equation for the problem in question  

Here Wq denotes the energy operator, consisting of the kinetic and the potential energy for a one-electron problem we have 

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