Quantum Mechanics: A Fundamental Approach

Kong Wan

June 30, 2018 Forthcoming by Pan Stanford
Textbook - 700 Pages
ISBN 9789814774659 - CAT# N12084

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A mathematically and physically self-contained reference source for the mathematics and physics of quantum mechanics

Adopts a geometric approach starting from three-dimensional vectors to help understand the abstract mathematics needed for quantum mechanics

Re-introduces various quantities and their properties in three-dimensional vector space in finite-dimensional and then in infinite-dimensional complex vectors spaces, thereby following an approach that is distinct from the traditional treatment which presents a discussion on Hilbert spaces from the very start

Devotes an exhaustive chapter to each group of postulates of quantum mechanics

Serves as the basic text for a separately published solutions manual, which presents the answers to all the questions given at the end of each chapter of the book


The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning. This makes it difficult to appreciate the mathematical formalism and hampers the understanding of quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics.

Quantum mechanics is presented in six groups of postulates. A chapter is devoted to each group of postulates with a detailed discussion. Systems with superselection rules, and some conceptual issues such as quantum paradoxes and measurement, are also discussed. The book concludes with several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov–Bohm effect.