Exclusion principle and quantum mechanics

There were 2 approaches to the difficult problems connected with the quantum of action.

1. An effort to bring abstract order to the new ideas.

This was done by looking for a key to translate classical mechanics and electrodynamics into quantum language. This would then form a logical generalization of these.

Bohr’s correspondence principle went for this.

2. A direct interpretation of the laws of spectra in terms of integral numbers.

This follows Kepler’s investigation of the planetary system through an inner feeling for harmony.

This was because of the difficulties which blocked the use of the concepts of kinematical models,

Sommerfeld preferred this.

I felt both methods were reconcilable.

The series of whole numbers 2, 8, 18, 32… giving the lengths of the periods in the natural system of chemical elements, was zealously discussed in Munich, including the remark of the Swedish physicist, Rydberg, that these numbers are of the simple form 2 n 2, if n takes on all integer values.

Sommerfeld tried especially to connect the number 8 and the number of corners of a cube. A new phase of my scientific life began when I met Niels Bohr personally for the first time.

This was in 1922, when he gave a series of guest lectures at Göttingen, in which he reported on his theoretical investigations on the Peri- odic System of Elements.

I shall recall only briefly that the essential progress made by Bohr’s considerations at that time was in explaining, by means of the spherically symmetric atomic model, the formation of the intermediate shells of the atom and the general properties of the rare earths.

Bohr had emphasized as a fundamental problem: Why were all electrons of an atom in its ground state not bound in the innermost shell?

I went to Copenhagen in the autumn of 1922 to explain the anomalous Zeeman effect.

It was the splitting of the spectral lines in a magnetic field which is different from the normal triplet.

On the one hand, the anomalous type of splitting exhibited beautiful and simple laws.

Landé had already succeeded to find the simpler splitting of the spectroscopic terms from the observed splitting of the lines.

The most fundamental of his results thereby was the use of half-integers as magnetic quantum numbers for the doublet-spectra of the alkali metals.

On the other hand, the anomalous splitting was hardly understandable from the mechanical model of the atom. This was because the general assumptions on the electron used both classical and quantum theory.

This always led to the same triplet.

But this led to 2 logically different difficulties simultaneously.

1. The absence of a general key to translate a given mechanical model into quantum theory.

2. Our ignorance on the proper classical model which derive at all an anomalous splitting of spectral lines emitted by an atom in an external magnetic field.

It is therefore not surprising that I could not find a satisfactory solution of the problem at that time.

I was able to generalize Landé’s term analysis for very strong magnetic fields.

This helped me to discover the exclusion principle.