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.

High Resolution NMR provides a broad treatment of the principles and theory of nuclear magnetic resonance (NMR) as it is used in the chemical sciences. It is written at an "intermediate" level, with mathematics used to augment, rather than replace, clear verbal descriptions of the phenomena. The book is intended to allow a graduate student, advanced undergraduate, or researcher to understand NMR at a fundamental level, and to see illustrations of the applications of NMR to the determination of the structure of small organic molecules and macromolecules, including proteins. Emphasis is on the study of NMR in liquids, but the treatment also includes high resolution NMR in the solid state and the principles of NMR imaging and localized spectroscopy. Careful attention is given to developing and interrelating four approaches - steady state energy levels, the rotating vector picture, the density matrix, and the product operator formalism. The presentation is based on the assumption that the reader has an acquaintance with the general principles of quantum mechanics, but no extensive background in quantum theory or proficiency in mathematics is required. Likewise, no previous background in NMR is assumed, since the book begins with a description of the basic physics, together with a brief account of the historical development of the field. This third edition of High Resolution NMR preserves the "conversational" approach of the previous editions that has been well accepted as a teaching tool. However, more than half the material is new, and the remainder has been revised extensively. Problems are included to reinforce concepts in the book. Uses mathematics to augment, not replace, verbal explanations Written in a clear and conversational style Follows the successful format and approach of two previous editions Revised and updated extensively--about 70 percent of the text is new Includes problems and references to additional reading at the end of each chapter

NMR has become the most diverse spectroscopic tool available to date in biomedical research. It is now routinely used to study biomolecular structure and dynamics particularly as a result of recent developments of a cascade of highly sophisticated multidimensional NMR pulse sequences, and of advances in genetic engineering to produce biomolecules, uniformly or selectively enriched with 13C, 15N and 2H. Features of this book: • Provides an up-to-date treatment of NMR techniques and their application to problems of biomedical interest • Most refined multidimensional pulse sequences including the basic aspects are covered by leading NMR spectroscopists. The book will be useful to NMR spectroscopists, biochemists, and to molecular biologists interested in the use of NMR techniques for solving biological problems.

The book provides a detailed account of how condensed-phase molecular dynamics are reflected in the line shapes of NMR spectra. The theories establishing connections between random, time-dependent molecular processes and lineshape effects are exposed in depth. Special emphasis is placed on the theoretical aspects, involving in particular intermolecular processes in solution, and molecular symmetry issues. The Liouville super-operator formalism is briefly introduced and used wherever it is beneficial for the transparency of presentation. The proposed formal descriptions of the discussed problems are sufficiently detailed to be implemented on a computer. Practical applications of the theory in solid- and liquid-phase studies are illustrated with appropriate experimental examples, exposing the potential of the lineshape method in elucidating molecular dynamics NMR-observable molecular phenomena where quantization of the spatial nuclear degrees of freedom is crucial are addressed in the last part of the book. As an introduction to this exciting research field, selected aspects of the quantum mechanics of isolated systems undergoing rotational tunnelling are reviewed, together with some basic information about quantum systems interacting with their condensed environment. The quantum theory of rate processes evidenced in the NMR lineshapes of molecular rotors is presented, and illustrated with appropriate experimental examples from both solid- and liquid-phase spectra. In this context, the everlasting problem of the quantum-to-classical transition is discussed at a quantitative level. The book will be suitable for graduate students and new and practising researchers using NMR techniques.