Introduction

Under this name at present two theories are being carried on, which are indeed closely related but not identical. The first, which follows on directly from the famous doctoral thesis by L. de Broglie, concerns waves in three-dimensional space. Because of the strictly relativistic treatment that is adopted in this version from the outset, we shall refer to it as the four-dimensional wave mechanics. The other theory is more remote from Mr de Broglie's original ideas, insofar as it is based on a wave-like process in the space of position coordinates (q-space) of an arbitrary mechanical system. We shall therefore call it the multi-dimensional wave mechanics. Of course this use of the q-space is to be seen only as a mathematical tool, as it is often applied also in the old mechanics; ultimately, in this version also, the process to be described is one in space and time. In truth, however, a complete unification of the two conceptions has not yet been achieved. Anything over and above the motion of a single electron could be treated so far only in the multi-dimensional version; also, this is the one that provides the mathematical solution to the problems posed by the Heisenberg–Born matrix mechanics. For these reasons I shall place it first, hoping in this way also to illustrate better the characteristic difficulties of the as such more beautiful four-dimensional version.