Synopses & Reviews
In many books about quantum mechanics for graduate students, only the unitary evolution, Hamiltonian systems and pure states are considered. In the suggested book, the modern mathematical concepts, which are the general for Hamiltonian and non-Hamiltonian systems, are used. It allows us to formulate the quantum mechanics of a wide class of systems, such as the open, non-Hamiltonian, dissipative, and nonlinear. Hamiltonian systems in pure states and its unitary evolution are considered as special cases of quantum theory.
1. The book is self-contained and can be used by students without a previous course in modern mathematics and physics. To read the text it is not required preliminary knowledge of graduate and advanced mathematics. All the necessary information, which is beyond undergraduate courses of the mathematics, is suggested in the book.
2. The suggested book can be used as an introduction to modern quantum mechanics for graduate students in physics and mathematics. The part of the book can be used in the lecture courses for undergraduate students. The other part has recent fundamental results that are not considered in monographs and text books.
3. The style of the book is oriented for mathematicians and physicists. For mathematicians, we use definitions and propositions. For physicists, the long and difficult proofs are not considered and the physical reasons to use the mathematical structures are discussed.
4. The book describes the structure of the modern theory. It has fundamental results of last 15 years. These results are not considered in the monographs and text-books.
5. If you would like to understand the mathematical structure of the modern quantum theory, then you must to buy the given book. The other books describe the quantum theory of first half of XX century or only small part of the modern structures.
6. The given book can be used for theoretical physics, quantum chemistry and quantum informatics courses for graduate level students. The manuscript can be useful not only for these graduate students but also for specialists in quantum chemistry and quantum informatics, nonlinear dynamics, chaos and complexity.
Synopsis
Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.
• Requires no preliminary knowledge of graduate and advanced mathematics
• Discusses the fundamental results of last 15 years in this theory
• Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences
About the Author
Vasily E. Tarasov was born in 1965. He received his M. S. in Physics from the Moscow State University in 1988. V. Tarasov received Ph.D. in Theoretical Physics from the Moscow State University in 1995. He was a Research Associate at the Skobeltsyn Institute of Nuclear Physics, Moscow State University for six years (1995-2001) and then became a Senior Research Associate at the Skobeltsyn Institute of Nuclear Physics, Moscow State University. Vasily E. Tarasov is an Associate Professor at the Applied Mathematics and Physics Department of Moscow Aviation Institute since 1998. He has published about 90 scientific works, among which 3 books and about 65 papers in refereed journals.
Skobeltsyn Institute of Nuclear Physics, Moscow State University and Applied Mathematics and Physics Department, Moscow Aviation Institute, Russia
Table of Contents
Part I. Quantum Kinematics
1. Quantum Kinematics of Bounded Observables
2. Quantum Kinematics of Unbounded Observables
3. Mathematical Structures in Quantum Kinematics
4. Spaces of Quantum Observables
5. Algebras of Quantum Observables
6. Mathematical Structures on State Sets
7. Mathematical Structures in Classical Kinematics
8. Quantization in Kinematics
9. Spectral Representation of Observable
Part II. Quantum Dynamics
10. Superoperators and its Properties
11. Superoperator Algebras and Spaces
12. Superoperator Functions
13. Semi-groups of Superoperators
14. Differential Equations for Quantum Observables
15. Quantum Dynamical Semi-Groups
16. Classical Non-Hamiltonian Dynamics
17. Quantization of Dynamical Structure
18. Quantum Dynamics of States
19. Dynamical Deformation of Algebras of Observables
20. Fractional Quantum Dynamics
21. Stationary States of non-Hamiltoniam Systems
22. Quantum Dynamical Methods
23. Path Integral for non-Hamiltoniam Systems
24. Non-Hamiltonian Systems as a Quantum Computers