Exclusion principle and quantum mechanics

The problem of the closing of the electronic shells was not clear.

The only thing that was clear was that a closer relation of this problem to the theory of multiplet structure must exist. I therefore tried to examine again critically the simplest case, the doublet structure of the alkali spectra.

According to the point of view then orthodox, which was also taken over by Bohr in his already mentioned lectures in Göttingen.

Classically Non-describable Two-valuedness

The belief was that the cause of this doublet structure was a non-vanishing angular momentum of the atomic core.

I rejected this.

In the autumn of 1924 I proposed instead a new quantum theoretic property of the electron, which I called a two-valuedness not describable classically.

Stoner made improvements in the classification of electrons in subgroups.

He said that for a given value of the principal quantum number is the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field the same as the number of electrons in the closed shell of the rare gases which corresponds to this principal quantum number.

On the basis of my earlier results on the classification of spectral terms in a strong magnetic field the general formulation of the exclusion principle became clear to me.

The fundamental idea is:

The complicated numbers of electrons in closed subgroups are reduced to the simple number one if the division of the groups by giving the values of the 4 quantum numbers of an electron is carried so far that every degeneracy is removed.

An entirely non-degenerate energy level is already « closed », if it is occupied by a single electron.

States in contradiction with this postulate have to be excluded.

The exposition of this general formulation of the exclusion principle was made in Hamburg in the spring of 1925 after I was able to verify some additional conclusions concerning the anomalous Zeeman effect of more complicated atoms during a visit to Tübingen with the help of the spectroscopic material assembled there.

The physicists found it difficult to understand the exclusion principle, since no meaning in terms of a model was given to the fourth degree of freedom of the electron.

The gap was filled by Uhlenbeck and Goudsmit’s idea of electron spin.

Through it, the anomalous Zeeman effect could be understood simply by assuming that:

• the spin quantum number of one electron is equal to 1⁄2
• the quotient of the magnetic moment to the mechanical angular moment has for the spin a value twice as large as for the ordinary orbit of the electron.

Since that time, the exclusion principle has been closely connected with the idea of spin.

I believed it through Thomas’ calculations on the magnitude of doublet splitting.

Bohr showed through wave mechanics that the electron spin cannot be measured by classical experiments such as through the deflection of molecular beams in external electromagnetic fields.

Therefore, my “classically non-describable two-valuedness” is essentially a quantum-mechanical property of the electron8,9.

In 1925, the same year in which I published my paper on the exclusion principle, De Broglie formulated his idea of matter waves and Heisenberg the new matrix-mechanics.

In the next year Schrödinger’s wave mechanics quickly followed.

Bohr used the idea of « complementarity » as a new central concept for these.

The statements of quantum mechanics are dealing only with possibilities, not with actualities.

They have the form:

• « This is not possible » or
• « Either this or that is possible »

But they can never say « That will actually happen then and there ».

The actual observation appears as an event outside the range of a description by physical laws.

It brings forth a discontinuous selection out of the several possibilities foreseen by the statistical laws of the new theory.*

The self-consistency of quantum theory had been lost since Planck’s discovery of the quantum of action.

• This self-consistency was reached again only after the old claims for an objective description of the physical phenomena, independent of the way they are observed, was renounced.