Written in a clear pedagogic style, this book deals with the application of density matrix theory to atomic and molecular physics. The aim is to precisely characterize sates by a vector and to construct general formulas and proofs of general theorems. The basic concepts and quantum mechanical fundamentals (reduced density matrices, entanglement, quantum correlations) are discussed in a comprehensive way. The discussion leads up to applications like coherence and orientation effects in atoms and molecules, decoherence and relaxation processes. This third edition has been updated and extended throughout and contains a completely new chapter exploring nonseparability and entanglement in two-particle spin-1/2 systems. The text discusses recent studies in atomic and molecular reactions. A new chapter explores nonseparability and entanglement in two-particle spin-1/2 systems.

During the last two decades the experimental investigation of atomic coherence phenomena has made rapid progress. Detailed studies have been performed of angular correlations, spin polarization effects, angular momen tum transfer, and the alignment parameters which characterize the charge cloud of excited atoms. The enormous growth in the number of these investigations was made possible through substantial development and application of new experimental technology, the development of sophisti cated theoretical models and numerical methods, and a fine interplay between theory and experiment. This interplay has resulted in a deeper understanding of the physical mechanisms of atomic collision processes. It is the purpose of the chapters in this book to provide introductions for nonspecialists to the various fields of this area as well as to present new experimental and theoretical results and ideas. The interest in spin-dependent interactions in electron-atom scattering has a long history; it dates back to the early investigations of Mott in 1929. While the more traditional measurements in this field were concerned with the determination of spin polarization and asymmetries, the range of investi gations has been expanded enormously during the last few years and now includes many observables sensitive to one or more of the various spin dependent interactions. The understanding of these effects requires a theoretical description of the orientation and alignment parameters of the target atoms, of the forma tion of resonances, of the influence of electron-exchange processes, and of the relativistic interactions inside the atom and between projectile and target."

During the last two decades the experimental investigation of atomic coherence phenomena has made rapid progress. Detailed studies have been performed of angular correlations, spin polarization effects, angular momen tum transfer, and the alignment parameters which characterize the charge cloud of excited atoms. The enormous growth in the number of these investigations was made possible through substantial development and application of new experimental technology, the development of sophisti cated theoretical models and numerical methods, and a fine interplay between theory and experiment. This interplay has resulted in a deeper understanding of the physical mechanisms of atomic collision processes. It is the purpose of the chapters in this book to provide introductions for nonspecialists to the various fields of this area as well as to present new experimental and theoretical results and ideas. The interest in spin-dependent interactions in electron-atom scattering has a long history; it dates back to the early investigations of Mott in 1929. While the more traditional measurements in this field were concerned with the determination of spin polarization and asymmetries, the range of investi gations has been expanded enormously during the last few years and now includes many observables sensitive to one or more of the various spin dependent interactions. The understanding of these effects requires a theoretical description of the orientation and alignment parameters of the target atoms, of the forma tion of resonances, of the influence of electron-exchange processes, and of the relativistic interactions inside the atom and between projectile and target."

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 variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely 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."