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.
About the Author:
Kong Wan is honorary reader in Theoretical Physics in St Andrews University, Scotland, UK. He studied theoretical physics in St Andrews, both as an undergraduate and a postgraduate, and was awarded a PhD in 1972. He stayed on in St Andrews and became a reader in Theoretical Physics. His research has focussed on the foundations and formalism of quantum mechanics.
This text is for graduate students who have had previous advanced undergraduate courses in quantum mechanics. The author has observed that students lack confidence with the mathematical formalisms of quantum mechanics. Consequently they cannot properly appreciate the complexities of the theory. The text addresses this by presenting the mathematics in its simplest form and then helping students develop an intuition for its use in quantum mechanics. This way the students are not lost in the mathematical abstractions. The book is well suited to this task. After a brief review of the fundamentals of classical and quantum systems, the majority of the book is offered in two sections. The first of these gives a very thorough presentation of the mathematical formalisms used in quantum mechanics. The second section details the quantum formalism. A final, relatively brief section considers applications. The author is successful in creating a resource that addresses his justifiable concerns about student understanding. This is a lot of material, and it may be best suited for a two-semester course. The first semester could cover the mathematics and the second the physics.~CHOICE