X Operator Quantum Mechanics
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Quantum Mechanics
Author: Louis Marchildon
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
Whoever begins writing a book on quantum mechanics is struck by the breadth of the subject. In its applications first: atomic and molecular p- sics, nuclear physics, optics, solid state physics, theory of gases and liquids, elementary particles theory, almost all fields of contemporary physics are based on quantum mechanics. In its formulation, also, which borrows from many subfields of mathematics and reaches philosophical reflection as much as modern technology. The writing therefore implies, at the outset, making choices. I first chose to write a book for those who strive to understand qu- tum mechanics. These are physics students, of course, but also students and investigators in theoretical chemistry, biophysics and engineering physics w- hing to comprehend more deeply the computational methods they use. I have thus tried to clarify delicate points rather than leave them aside. Conceptual problems are treated in more detail than in most general textbooks. But understanding also involves the capability to perform concrete calculations. This motivates the development of numerical methods which, most of the time, are the only ones that yield quantitative results. I chose also to present quantum mechanics as a self-contained theory. The exposition largely develops around the central notion of state space.
Visual Quantum Mechanics
Author: Bernd Thaller
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-05-08
"Visual Quantum Mechanics" uses the computer-generated animations found on the accompanying material on Springer Extras to introduce, motivate, and illustrate the concepts explained in the book. While there are other books on the market that use Mathematica or Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner. There is no special emphasis on computational physics or requirement that the reader know a symbolic computation package. Despite the presentation of rather advanced topics, the book requires only calculus, making complicated results more comprehensible via visualization. The material on Springer Extras provides easy access to more than 300 digital movies, animated illustrations, and interactive pictures. This book along with its extra online materials forms a complete introductory course on spinless particles in one and two dimensions.
Quantum Mechanics
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.