Foundations of Quantum Mechanics I

This book is the first volume of a two-volume work on the Foundations of Quantum Mechanics, and is intended as a new edition of the author's book Die Grundlagen der Quantenmechanik [37] which was published in 1954. In this two-volume work we will seek to obtain an improved formulation of the interpretation of quantum mechanics based on experiments. The second volume will appear shortly.
Since the publication of [37] there have been several attempts to develop a basis for quantum mechanics which is, in the large part, based upon the work of J. von Neumann [38]. In particular, we mention the books of G. W. Mackey [39], J. Jauch [40], C. Piron [41], M. Drieschner [9], and the original work of S. P. Gudder [42], D. J. Foulis and C. H. Randall [43], and N. Zierler [44]. Here we do not seek to compare these different formulations of the foundations of quantum mechanics. We refer interested readers to [45] for such comparisons.
In this book we shall seek only to develop a well-defined formulation for the foundations of quantum mechanics and to examine the implications of such a formulation towards the most important applications of quantum mechanics in a consistent manner. This formulation will be based only on the objective, that is, the so-called classical mode of description of the apparatuses. In this respect this book represents a systematic mathematical, as well as conceptual, formulation of the original viewpoint of N. Bohr in which it is assumed that it is necessary to use the classical mode of description in order to describe the measurement process in quantum mechanics (see, for example, the extensive discussion in M. Jammer and E. Scheibe [14]).