Format:
Online Ressource (1 volume)
Edition:
Online-Ausg.
ISBN:
9780444530912
,
0444530916
,
9780080559711
,
0080559719
,
1281279633
,
9781281279637
Series Statement:
Monograph series on nonlinear science and complexity v. 7
Content:
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
Note:
Includes bibliographical references and index. - Print version record
,
Cover; Preface; Contents; A Very Few Preliminaries; 1. Potential and conservative systems; 2. Hamiltonian and non-Hamiltonian classical systems; 3. Examples of non-Hamiltonian systems; 4. Non-Hamiltonian and dissipative classical systems; 5. Non-Hamiltonian and dissipative quantum systems; 6. Quantization of non-Hamiltonian and dissipative systems; Part I: Quantum Kinematics; Chapter 1. Quantum Kinematics of Bounded Observables; 1.1. Observables and states; 1.2. Pre-Hilbert and Hilbert spaces; 1.3. Separable Hilbert space; 1.4. Definition and examples of operators
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1.5. Quantum kinematical postulates1.6. Dual Hilbert space; 1.7. Dirac's notations; 1.8. Matrix representation of operator; Chapter 2. Quantum Kinematics of Unbounded Observables; 2.1. Deficiencies of Hilbert spaces; 2.2. Spaces of test functions; 2.3. Spaces of generalized functions; 2.4. Rigged Hilbert space; 2.5. Linear operators on a rigged Hilbert space; 2.6. Coordinate representation; 2.7. X-representation; Chapter 3. Mathematical Structures in Quantum Kinematics; 3.1. Mathematical structures; 3.2. Order structures; 3.3. Topological structures; 3.4. Algebraic structures
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3.5. Examples of algebraic structures3.6. Mathematical structures in kinematics; Chapter 4. Spaces of Quantum Observables; 4.1. Space of bounded operators; 4.2. Space of finite-rank operators; 4.3. Space of compact operators; 4.4. Space of trace-class operators; 4.5. Space of Hilbert-Schmidt operators; 4.6. Properties of operators from K1 (H) and K2 (H); 4.7. Set of density operators; 4.8. Operator Hilbert space and Liouville space; 4.9. Correlation functions; 4.10. Basis for Liouville space; 4.11. Rigged Liouville space; Chapter 5. Algebras of Quantum Observables; 5.1. Linear algebra
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5.2. Associative algebra5.3. Lie algebra; 5.4. Jordan algebra; 5.5. Involutive, normed and Banach algebras; 5.6. C*-algebra; 5.7. W*-algebra; 5.8. JB-algebra; 5.9. Hilbert algebra; Chapter 6. Mathematical Structures on State Sets; 6.1. State as functional on operator algebra; 6.2. State on C*-algebra; 6.3. Representations C*-algebra and states; 6.4. Gelfand-Naimark-Segal construction; 6.5. State on W*-algebra; Chapter 7. Mathematical Structures in Classical Kinematics; 7.1. Symplectic structure; 7.2. Poisson manifold and Lie-Jordan algebra; 7.3. Classical states
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7.4. Classical observables and C*-algebraChapter 8. Quantization in Kinematics; 8.1. Quantization and its properties; 8.2. Heisenberg algebra; 8.3. Weyl system and Weyl algebra; 8.4. Weyl and Wigner operator bases; 8.5. Differential operators and symbols; 8.6. Weyl quantization mapping; 8.7. Kernel and symbol of Weyl ordered operator; 8.8. Weyl symbols and Wigner representation; 8.9. Inverse of quantization map; 8.10. Symbols of operators and Weyl quantization; 8.11. Generalization of Weyl quantization; Chapter 9. Spectral Representation of Observable; 9.1. Spectrum of quantum observable
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9.2. Algebra of operator functions
Additional Edition:
ISBN 0444530916
Additional Edition:
ISBN 1281279633
Additional Edition:
Erscheint auch als Druck-Ausgabe Tarasov, Vasily E Quantum mechanics of non-Hamiltonian and dissipative systems Amsterdam ; Oxford : Elsevier, 2008
Language:
English
Keywords:
Electronic books
;
Electronic books
Author information:
Tarasov, Vasilij E. 1965-
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