Density Matrix Theory and Applications

Density Matrix Theory and Applications

by Karl Blum
     
 

ISBN-10: 0306406845

ISBN-13: 9780306406843

Pub. Date: 09/01/1981

Publisher: Basic Books

Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a

Overview

Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari­ ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Product Details

ISBN-13:
9780306406843
Publisher:
Basic Books
Publication date:
09/01/1981
Series:
Physics of Atoms and Molecules Series
Pages:
230

Table of Contents

1. Basic Concepts.- 2. General Density Matrix Theory.- 3. Coupled Systems.- 4. Irreducible Components of the Density Matrix.- 5. Radiation from Polarized Atoms. Quantum Beats.- 6. Some Applications.- 7. Quantum Theory of Relaxation.- Appendixes.- A: The Direct Product.- B: State Multipoles for Coupled Systems.- C: Formulas from Angular Momentum Theory.- D: The Efficiency of a Measuring Device.- E: The Scattering and Transition Operators.- References.

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