A way of understanding the laws which govem the worId of elementary particIes has not been found yet. Present-day theoretical physicists have to be satisfied with compromises which, at the best, promise some success at the expense of generality and unity. U nder these circumstances a critical analysis of the basic concepts of modem quantum theory may be timely and usefuI. It is hoped that the value of such an analysis may be preserved even if, in the near future, new ways of understanding the basis of elementary particIe physics are discovered. In this monograph one specific aspect of this analysis is treated, namely the problems of geometry in the microworld. An out- line of geometrical measurements in the macroworld was given pre- viously. These measurements seem to be c1ear enough for at least a certain set of problems to be considered as a starting point for discussing the situation in the microworld. The concepts and methods which are useful in the macroworld may only indirectly be carried over into the microworld and they require a high degree of abstraction. In comprehending the physical content of dynamic variables which have geometric meaning, for example, the space-time partic1e coor- dinates x, y, z, t it is of ten necessary to have recourse to gedanken experiments which, although not feasible in practice, can nevertheless be compatible with the basic principles of geometry and quantum mechanics.

The present monograph is devoted to the principal problems of quantum mechanics and is based on the conception first stated in my course on 'Fundamentals of Quantum Mechanics'. The scope and purpose of the above course did not allow some principal questions to be brought out as fully as they deserved, and besides, some important points were only very recently developed to a sufficient extent. This refers especially to the analysis of the action of the measuring instrument, whose dual role as an analyser of a quantum ensemble and as a detector of individual events was insufficiently elucidated. The reader will find that the present monograph is concerned more with theoretical physics than with philosophy. However, I have never separated Weltanschauung from science (and particularly theoretical physics) so that the philosophical implications are also discussed, justi fying publication in the philosophical series. In conclusion, I should like to thank the publisher and the translator, whose initiative and effort have made it possible for the book to reach the English-speaking reader."

The English translation of Osnovy kvantovol mekhaniki has been made from the third and fourth Russian editions. These contained a number of important additions and changes as compared with the first two editions. The main additions concern collision theory, and applications of quantum mechanics to the theory of the atomic nucleus and to the theory of elementary particles. The development of these branches in recent years, resulting from the very rapid progress made in nuclear physics, has been so great that such additions need scarcely be defended. Some additions relating to methods have also been made, for example concerning the quasiclassical approxi mation, the theory of the Clebsch-Gordan coefficients and several other matters with which the modern physicist needs to be acquainted. The alterations that have been made involve not only the elimination of obviously out-of-date material but also the refinement of various formulations and statements. For these refinements I am indebted to many persons who at different times have expressed to me their critical comments and suggestions. Particularly important changes have been made regarding the definition of a quantum ensemble in Section 14."

The present monograph is devoted to the principal problems of quantum mechanics and is based on the conception first stated in my course on 'Fundamentals of Quantum Mechanics'. The scope and purpose of the above course did not allow some principal questions to be brought out as fully as they deserved, and besides, some important points were only very recently developed to a sufficient extent. This refers especially to the analysis of the action of the measuring instrument, whose dual role as an analyser of a quantum ensemble and as a detector of individual events was insufficiently elucidated. The reader will find that the present monograph is concerned more with theoretical physics than with philosophy. However, I have never separated Weltanschauung from science (and particularly theoretical physics) so that the philosophical implications are also discussed, justi fying publication in the philosophical series. In conclusion, I should like to thank the publisher and the translator, whose initiative and effort have made it possible for the book to reach the English-speaking reader."