Quantum Mechanical Background

Abstract

To make this book self-contained and accessible to a broader audience, we begin with an outline of the mathematical framework of quantum theory, introducing vector spaces and linear operators, the postulates of quantum mechanics, the Schrödinger equation, and the density operator. In order to illustrate as well as motivate much of the discussion, we review the properties of the simplest, yet very important quantum mechanical system—the quantized harmonic oscillator, which is encountered repeatedly in the sections that follow.

Our presentation of the fundamental principles of quantum theory follows the traditional approach based on the standard set of postulates found in most textbooks. It could be viewed as a “pragmatic” approach in which quantum mechanics is accepted as an operational theory geared to predicting the outcomes of measurements on physical systems under well defined conditions. We have deliberately stayed clear of, depending on disposition, semiphilosophical issues pertaining to the relation of quantum theory and some of its counterintuitive notions vis a vis our macroscopic experience. Thus issues such as the collapse of the wavefunction upon measurement; the quantum correlations—entanglement—between spatially separated systems, or else, the non-local character of such correlations; the transition from the quantum to the classical world; etc., are treated according to the rules of the theory, without any excursion into philosophical implications, as they would be beyond the scope, as well as the needs, of this book. Discussions pertaining to such issues can be found in the relevant literature cited at the end of this book under the title Further Reading.