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This book presents an introduction to quantum mechanics that consistently uses the methods of operator theory, allowing readers to develop a physical understanding of quantum mechanical systems. The methods of operator theory are discussed throughout the book and presented with a mathematically rigorous approach. The author describes in detail how to use the methods of operator theory for analyzing quantum mechanical systems, starting with the definition of the involved physical operators (observables) up to the calculation of their spectra, spectral measures, and functional calculus. In addition, the book includes the construction of exponential functions of the involved Hamilton operators that solve the problem of time evolution.
Introduction.
Conventions.
A Short Summary of the Quantization Process.
List of Symbols.
Quantization of a Free Particle in N-Dimensional Space.
Commutators, Symmetries and Invariances.
Simple Quantum Systems in 1 Space Dimension.
Motion in a Central Force Field.
Motion in an Axially-Symmetric Force Field.
The Path Integral Approach to Quantum Mechanics.
Conclusion.
References.
Index