The Reasoning of Quantum Mechanics: Operator Theory and the Harmonic Oscillator

by Horst R. Beyer

Overview

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.

Product Details

ISBN-13:	9783031705090
Publisher:	Springer Nature Switzerland
Publication date:	11/22/2024
Series:	Synthesis Lectures on Engineering, Science, and Technology
Edition description:	Second Edition 2025
Pages:	98
Product dimensions:	6.61(w) x 9.45(h) x (d)

About the Author

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.

Table of Contents

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