Applieation of the Riemannian Geometry of the Complex Space to Ware-Mechanical Problems

抄録

On the basis of the author's theory of the electron an equation analogous to the wave-equation in wave-rnechanies was obtained in a precious paper. Now thus nethod of deriving it his been improved, by means of which we out interpret the wave-function precisely as the square root of the energy denaity in the eleatron. However on working coat further calculation with this modifled equation, some diffenlties have been experiential. The Rieituannian geometry id the complex space has been introduced to get rid of these diffieulties It is a generalisstion of the ordinary Riemannian geonetry, but low a characteristic in dealing with the linear differential front as fundlantental. Further the generalized quaternion units are used in place of the Dirae numbeas as distinguishing factors of the four-beins. We code that enabled to derive in a natural way a pair of wave-equations, each depending tat the eomplex value of the enerty density and its conjugate respectively. and also to show the legitinmey of the field-equations hitherto used in our investgation