The Fourth Electronic Degree of Freedom

THE FOURTH ELECTRONIC DEGREE OF FREEDOM The Stern-Gerlach Experiment... 

The origin of this magnetic moment was not clear in 1922. In its electronic ground state, a silver atom does not possess a spatial angular momentum, and the concept of an intrinsic electronic angular momentum (the electron spin) was yet to be created. In 1925, Goudsmit and Uhlenbeck introduced a fourth (spin) electron degree of freedom—in addition to the three spatial coordinates (x, y, z)—as a model to ease the explanation of the anomalous Zeeman effect.3,4... 

The postulate of a fourth independent quantum number was difficult to understand, since electrons were assumed to have only three—the spatial—degrees of freedom. 

In 1926 it was realized that there is a property of the electron other than the charge which must be taken into account, namely, the magnetic moment associated with intrinsic spin. It was shown by Goudsmit and Uhlenbeck [53] that this property, which represents an extra degree of freedom and therefore demands a fourth quantum number, could account for the doublet structure of the alkali spectra and the anomalous Zeeman effect. If was necessary and sufficient that the extra quantum number he two-valued. 

We have examined three forms of energy in molecules electronic, vibrational, and rotational. A fourth form, translational energy, has already been treated by the case of the three-dimensional box potential in Part I. Our findings for these degrees of freedom allow us to compose the parameter summary for HF given in Table 9.3. 

In fact the fourth quantum number does not emerge from solving Schrodinger s equation. It was initially introduced for experimental resons by Pauli, as a fourth degree of freedom possessed by each electron. In the later treatment by Dirac the fourth quantum number emerges in a natural manner. 

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