This book presents and details the process of quantization of a classical mechanical system in a relevant physical system, the harmonic oscillator. In quantum field theory or general relativity, mathematics and physics are inextricably interwoven. As such, the book is mathematically rigorous. The author focuses on the properties of the quantum system that can be observed and measured and interprets the resulting theory. The methods of operator theory are discussed throughout in the formulation of the theory as well as in the calculation of the consequences of the theory. The book addresses the mathematical support of the probabilistic interpretation of quantum mechanics through the spectral theorems for (densely-defined and linear) self-adjoint operators in Hilbert spaces. Considerable focus is placed on the measurement process and questions the challenges of the wave function, the EPR paradox, and Bell’s inequality.
Introduction.- The Classical Mechanical System.- The Corresponding
Quantum System.- Appendix.
Horst R. Beyer, Ph.D., is affiliated with the University of Tuebingen in Germany. Dr. Beyer has written numerous published articles in his areas of research interest, which include mathematical physics, in particular the applications of operator theory in quantum field theory, general relativity, astrophysics, and the engineering sciences.
