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, which makes it difficult to
appreciate the mathematical formalism and understand 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. This book is divided into four parts. Part I is a
brief review of the general properties of classical and quantum
systems. A general discussion of probability theory is also included
which aims to help in understanding the probability theories relevant
to quantum mechanics. Part II is a detailed study of the mathematics
for quantum mechanics. Part III presents quantum mechanics in a series
of postulates. Six groups of postulates are presented to describe
orthodox quantum systems. Each statement of a postulate is
supplemented with a detailed discussion. To make them easier to
understand, the postulates for discrete observables are presented
before those for continuous observables. Part IV presents several
illustrative applications, which include harmonic and isotropic
oscillators, charged particle in external magnetic fields and the
Aharonov–Bohm effect. For easy reference, definitions, theorems,
examples, comments, properties and results are labelled with section
numbers. Various symbols and notations are adopted to distinguish
different quantities explicitly and to avoid misrepresentation.
Self-contained both mathematically and physically, the book is
accessible to a wide readership, including astrophysicists,
mathematicians and philosophers of science who are interested in the
foundations of quantum mechanics.
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Produktdetaljer
ISBN
9781351333351
Publisert
2018
Utgave
1. utgave
Utgiver
Vendor
Jenny Stanford Publishing
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter