The electron as a vector wave

Abstract

In an article in ‘Nature’ last February I put forward a suggestion, of necessity in so concise a form as to be not very easily intelligible, that when the magnetic properties of the atom are regarded from the point of view of the wave mechanics, they suggest that the electron is to be taken as a wave of two components, like light, not of one like sound. The theory and its mathematical development were only outlined in ‘Nature,’ and the object of the present work is to give them in fuller detail. Recently Pauli has published a paper on the same subject, and arrived at the same mathematical results, but owing to the fact that he is more disposed to regard the wave theory as a mathematical convenience and less as a physical reality, he stops short of the point which was the guiding principle to me, and refuses to interpret the two functions that we both obtain as formed from a vector. I shall therefore here develop somewhat fully the arguments and analogies which seem to me to show that the vector is the right form in which to regard it. The chief part of the paper is concerned with developing the results given in ‘Nature’; owing to other work I have not carried the matter much farther yet. The main new points are general formulæ for the intensities of spectral lines, and for the magnetic moment, and the form the theory must take for several electrons—in which my first suggestion was wrong, and which Pauli has developed from his point of view. In a future paper I hope to discuss the motion of a free electron in a magnetic field, together with other problems. Since writing the account of the theory in ‘Nature’ I have had the immense benefit of a visit to Prof. Bohr’s Institute in Copenhagen, and have thus enjoyed the advantage of discussing the subject with him, Dr. Klein and the other members in detail. I may take the opportunity here to express my thanks to them for their interest in the matter and for many helpful criticisms.