Fain Irreversibilities in Quantum Mechanics

1. Auflage 2006
ISBN: 978-0-306-47128-5
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 113, 224 Seiten, eBook

Reihe: Fundamental Theories of Physics

The problem of irreversibility is ubiquitous in physics and chemistry. The present book attempts to present a unified theoretical and conceptual framework for the description of various irreversible phenomena in quantum mechanics. In a sense, this book supplements conventional textbooks on quantum mechanics by including the theory of irreversibilities. However, the content and style of this book are more appropriate for a monograph than a textbook. We have tried to arrange the material so that, as far as possible, the reader need not continually refer elsewhere. The references to the literature make no pretense of completeness. The book is by no means a survey of present theoretical work. We have tried to highlight the basic principles and their results, while the attention has been mainly paid to the problems in which the author himself has been involved. The book as a whole is designed for the reader with knowledge of theoretical physics (especially quantum mechanics) at university level. This book is based on the courses of lectures given at the Chemistry Department of Tel-Aviv University.

Zielgruppe

Research

Autoren/Hrsg.

Fain, B.

Fain, Benjamin

Inhaltsverzeichnis

Quantum-Theoretical Basis. Density Matrix.- Quantum Theory of Relaxation Processes.- Interaction with Phonons and Molecular Vibrations.- Interaction with Photons.- Memory Effects in Relaxation Processes, Exact Solutions.- Quantum Measurement and Irreversibility.

Leseproben

CHAPTER 1 QUANTUM-THEORETICAL BASIS. DENSITY MATRIX (p. 1-2)

The present chapter gives a short account of the basic concepts of quantum theory. Since our main purpose is quantum theory of irreversible processes, the use of the density matrix concept is indispensable. A conventional presentation of quantum theory principles uses the wave function as the basic characteristic of a quantum system. In this case the density matrix is, in a sense, a derivative of the wave function. In this chapter we consider the density matrix as a basic, primary characteristic of the quantum system [1], while the description by the wave function is a specific case of the description with aid of the density matrix. We realize that such an approach is a generalization of the conventional procedure. However, this generalization seems to be quite natural, and only due to historical reasons quantum theory text books use the wave function presentation. In this chapter we follow conventional (Copenhagen) interpretation of quantum mechanics. A different approach will be considered in the last chapter (Chapter VI).

1.1 Basic concepts

The nature of the phenomena occurring at the atomic level is very different from the nature of the phenomena of the macrocosm. For this reason the basic concepts of the classical theory proved to be invalid in describing the microcosm. The concept of the state of a physical system underwent a most radical re-examination. In classical physics it is assumed that the physical quantities (or properties of a system) found from various measurements made on a system are characteristics of the particular state of the system, that they are always present in a given system in a definite form and that this does not depend on the observational methods and equipment. In quantum physics they are at the same time characteristics of the methods and equipment used for the observations. In the microcosm we cannot ignore the effect of the measuring apparatus on the measured object. Therefore the concept of the quantum state takes into account both the object which is in this state and possible experimental devices used to make the measurement. Accordingly, the quantum theoretical description of quantum objects differs essentially from the classical description. Quantum theory, unlike the classical theory, is a statistical theory in principle. The laws of quantum theory do not govern the actual behavior of a particular object, but give the probabilities of the various ways in which the object may behave as a result of an interaction with its surroundings. The following postulates form the basis of the quantum description of physical phenomena.