Free motion in the wave mechanics

Abstract The present work is a discussion of a number of simple problems of the free motion of electrons and atoms from the point of view of the wave mechanics. The author has had the advantage of many conversations with Prof. N. Bohr on the subject, and it was composed under this inspiration. Bohr has recently published his views on the foundations of the theory, and it would be out of place to enter here deeply into the matter, but some review of principles is unavoidable if the technical processes are to be understood. Perhaps the chief point of the work is to show how a simple, even old-fashioned, technique is entirely adequate to deal with these very new problems. 1. General Principles. The matrix and the wave mechanics have both been already developed to great lengths as a calculus of stationary states, but they have not yet got so far in what we may call dynamics, a description of the progress of events. More and more complicated phenomena have been fitted into the same scheme, but not much has been done in making this scheme intuitively understandable. One of the most important contributions is a recent work by Heisenberg, who develops an “uncertainty relation” by showing how each observation of a system, say an electron, always itself introduces some disturbance, so that the exact state at the beginning of each new experiment is essentially unknowable. Heisenberg works from the matrix point of view, but Bohr has pointed out that the “uncertainty relation,” exhibited by Heisenberg simply as an experi­mental result, becomes quite natural on wave principles, and is indeed nothing more than an expression of those principles.