Arno Bohm – författare

This edition differs from the second chiefly in the addition of about tOO pages devoted to the quantum (or geometric, or Berry) phase, a subject that did not exist when this book was written. The changes in the remainder of the book consist of corrections of a small number of misprints. While it may seem that adding two chapters on the quantum phase is overemphasizing a currently fashionable subject, they actually complete the development of quantum theory as given in this book. We start with simple models, synthesizing them into complicated "molecules." With the new chap­ ters, we end with complicated "molecules," dividing them into simpler parts. This process of dividing a complex system into parts quite naturally gives rise to a gauge theory, of which the geometric phase is a manifestation - with consequences not only in theory, but observable in experiments. For this rea­ son, the geometric phase is not a mere fashion, but a discovery that will retain its importance forever and must be discussed in textbooks on quantum mechanics. I would like to acknowledge help and advice from Mark Loewe with the writing and also of the new part of the book. In addition, I would like to express my gratitude to J. Anandan, M. Berry, and C.A. Mead, who have read parts or all of the new material and have provided valuable advice.

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.

The first edition of this book was written as a text and has been used many times in a one-year graduate quantum mechanics course. One of the reviewers has made me aware that the book can also serve as, " . . . in principle, a handbook of nonrelativistic quantum mechanics. " In the second edition we have therefore added material to enhance its usefulness as a handbook. But it can still be used as a text if certain chapters and sections are ignored. We have also revised the original presentation, in many places at the suggestion of students or colleagues. As a consequence, the contents of the book now exceed the material that can be covered in a one-year quantum mechanics course on the graduate level. But one can easily select the material for a one-year course omitting-according to one''s preference-one or several of the following sets of sections: {1. 7, XXI}, {X, XI} or just {XI}, {II. 7, XIII}, {XIV. 5, XV}, {XIX, XX}. Also the material of Sections 1. 5-1. 8 is not needed to start with the physics in Chapter II. Chapters XI, XIII, XIX, and XX are probably the easiest to dispense with and I was contemplating the deletion of some of them, but each chapter found enthusiastic supporters among the readers who advised against it. Chapter I-augmented with some applications from later chapters-can also be used as a separate introductory text on the mathematics of quantum mechanics.

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.

Dirac's formalism of quantum mechanics was always praised for its elegance. This book introduces the student to its mathematical foundations and demonstrates its ease of applicability to problems in quantum physics. The book starts by describing in detail the concept of Gel'fand triplets and how one can make use of them to make the Dirac heuristic approach rigorous. The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Next, the RHS model for decaying states based on the concept of Gamow vectors is presented. Applications are given to physical theories of such phenomena as decaying states and resonances.

This volume has its origin in the Semigroup Symposium which was organized in connection with the 21st International Colloquium on Group Theoretical Methods in Physics (ICGTMP) at Goslar, Germany, July 16-21, 1996. Just as groups are important tools for the description of reversible physical processes, semigroups are indispensable in the description of irreversible physical processes in which a direction of time is distinguished. There is ample evidence of time asymmetry in the microphysical world. The desire to go beyond the stationary systems has generated much recent effort and discussion regarding the application of semigroups to time-asymmetric processes. The book should be of interest to scientists and graduate students

This is an introductory graduate course on quantum mechanics, which is presented in its general form by stressing the operator approach. Representations of the algebra of the harmonic oscillator and of the algebra of angular momentum are determined in chapters 1 and 2 respectively. The algebra of angular momentum is enlarged by adding the position operator so that the algebra can be used to describe rigid and non-rigid rotating molecules. The combination of quantum physical systems using direct-product spaces is discussed in chapter 3. The theory is used to describe a vibrating rotator, and the theoretical predictions are then compared with data for a vibrating and rotating diatomic molecule. The formalism of first- and second-order non-degenerate perturbation theory and first-order degenerate perturbation theory are derived in chapter 4. Time development is described in chapter 5 using either the Schroedinger equation of motion or the Heisenberg’s one. An elementary mathematical tutorial forms a useful appendix for the readers who don’t have prior knowledge of the general mathematical structure of quantum mechanics.

This is an introductory graduate course on quantum mechanics, which is presented in its general form by stressing the operator approach. Representations of the algebra of the harmonic oscillator and of the algebra of angular momentum are determined in chapters 1 and 2 respectively. The algebra of angular momentum is enlarged by adding the position operator so that the algebra can be used to describe rigid and non-rigid rotating molecules. The combination of quantum physical systems using direct-product spaces is discussed in chapter 3. The theory is used to describe a vibrating rotator, and the theoretical predictions are then compared with data for a vibrating and rotating diatomic molecule. The formalism of first- and second-order non-degenerate perturbation theory and first-order degenerate perturbation theory are derived in chapter 4. Time development is described in chapter 5 using either the Schroedinger equation of motion or the Heisenberg’s one. An elementary mathematical tutorial forms a useful appendix for the readers who don’t have prior knowledge of the general mathematical structure of quantum mechanics.