This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory,...
This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a r...
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its...
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction its...
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes th...
Are you looking for a concise summary of the theory of Schrodinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don t just cover general properties, but also detail multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.
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Are you looking for a concise summary of the theory of Schrodinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb,...
Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.
Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillato...
The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is...
The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theo...
A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of...
A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of su...
