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This book provides important and relevant theories in quantum mechanics. Human understanding regarding the universe and nature driven forces have been thoroughly influenced by the Quantum theory as a scientific revolution. Possibly, the historical advancement of this concept mimics the history of human scientific endeavors from their birth. The book presents a valuable account of foundation, scientific history of the concept, distinct techniques to solve the Schrodinger equation, and relativistic quantum mechanics and field theory. Some of the important topics are complementarity in quantum mechanics & classical statistical mechanics, and theory of elementary particles based on Newtonian mechanics. The aim of this book is to serve as an efficient reference for researchers and students.
Introduction to Quantum Statistical Mechanics (2nd Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.
This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space — such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz — can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.
This book is a very early systematic treatment of the application of the field-theoretical methods developed after the Second World War to the quantum mechanical many-body problem at finite temperature. It describes various techniques that remain basic tools of modern condensed matter physicists.
This text represents the first translated edition of a special series of lectures delivered at the Physics Department of the Moscow State University.It can serve as an introduction to a large group ranging from final year undergraduates to researchers and others requiring and understanding of Quantum Statistics and Second Quantization methods.
The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight the characteristics of the partition function and its application to the analysis of perfect and imperfect gases, solids, and dense fluids. These topics are followed by discussions on the fundamentals of quantum statistics, with particular emphasis on its application in certain media. The last chapter outlines the derivation of the relations between the partition functions and the thermodynamic quantities. This book will be of value to physical chemists, chemical physicists, mathematicians, and researchers in the allied fields of statistical mechanics.
This extensive reference text summarizes the concepts and mathematical methods that are required to provide a firm foundation for advanced studies in quantum thermal physics, which underlies all current mesoscopic sciences. The book introduces the mathematical language and fundamental physical concepts on which the entire subject of quantum statistical mechanics has been developed. Starting from the essential mathematical concepts, definitions, theorems, and formulas for the understanding and application of quantum statistical mechanics and physical sciences in general, the author provides pedagogical annotations to introduce new insights not to be found in traditional mathematics handbooks. Each chapter is completed with a set of further reading references which contain more complete treatment of the subjects described. This comprehensive volume will serve as a text throughout advanced studies in quantum statistical physics and beyond, and as a reference for researchers in all fields of physics.