It is the purpose of this article to show in outline how some of the basic ideas of quantum scattering theory can be used to supplement the usual topics covered in elementary quantum chemistry.
This book represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to specific applications. The formulation of quantum theory is explained and supported with illustrations of the general concepts of elementary quantum systems. In addition to traditional topics of nonrelativistic quantum mechanics - including single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, and the theory of angular momentum - the book also covers modern issues, among them quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is also outlined in explanatory notes. Ideal as a supplement to classroom lectures, the book can also serve as a compact and comprehensible refresher of elementary quantum theory for more advanced students.
Abstract This book provides an introduction to quantum theory, primarily for mathematics students. It assumes a knowledge of basic algebra and elementary group theory, with little or no familiarity with more advanced topics. Although it takes a traditional approach, the book exploits ideas of linear algebra and points out some of the mathematical subtleties of the theory. It also covers such topics as Bell's inequalities and coherent and squeezed states, and introduces group representation theory, algebraic quantum theory, and quantum statistical mechanics. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group-theoretical standpoint.
We present the basic ideas about the broad topic of molecular interactions in the context of low-energy collisions. We start by introducing the concept of the interaction energy and the crucial approximation behind it—the Born–Oppenheimer approximation. Next, we focus on understanding of molecular interactions within the framework of the perturbation theory. We discuss the essentials of symmetry-adapted perturbation theory (SAPT) which provides partitioning of the interaction energy into physically meaningful components, such as electrostatic, dispersion, induction, and exchange interactions. We examine the role of these components and how they can be calculated. We also discuss the supermolecular approach to calculation of the interaction energy with various quantum chemistry methods. We indicate potential pitfalls of the latter approach and give recommendations on how to alleviate them. To illustrate the theory presented in this chapter, we provide a detailed discussion of interactions within several systems of relevance in cold chemistry and cold collisions: He-NH(3Σ−), N-NH, He-OH(2Π), NH-NH, O2(3Σ−g)-O2. The calculations of collision rates and scattering cross-sections impose stringent requirements on the accuracy of the potential energy surfaces. To address the issue, we present the analysis of the scattering length dependence upon the potential scaling. Finally, we indicate trends in calculations of intermolecular forces stimulated by the state-of-the-art cold chemistry experiments.