This Second Edition presents and details the process of quantization of a classical mechanical system in a relevant physical system, the harmonic oscillator. As mathematics and physics are inextricably interwoven in quantum theories, the author takes a mathematically rigorous approach. The book focuses on properties of the quantum system that can be observed and measured, and the author then interprets the resulting theory. The book covers methods of operator theory in the formulation of the theory as well as in the calculation of the consequences of the theory. The author addresses the mathematical foundation of the probabilistic interpretation of quantum mechanics through the spectral theorems for (densely-defined and linear) self-adjoint operators in complex Hilbert spaces. The book also explains the measurement process and questions the challenges of the wave function, the EPR paradox, and Bell's inequality.

Presents the process of quantization of the harmonic oscillator and includes the necessary mathematics Develops and uses the language and basic results of operator theory via calculations, proofs, and exercises Focuses on the properties of the quantum system that can be observed, measured, and interpreted

Autorentext

Horst R. Beyer, Ph.D., is currently affiliated with the University of Tuebingen Institute for Astronomy and Astrophysics, Theoretical Astrophysics Division. Dr. Beyer has written 7 books and 39 published articles. His research interests include mathematical physics, in particular the applications of operator theory in quantum field theory, general relativity, astrophysics, and the engineering sciences.

Inhalt

Introduction.- The Classical Mechanical System.- The Corresponding Quantum System.- Conclusion.