Dynamical invariants, adiabatic approximation, and the geometric phase /
Saved in:
| Author / Creator: | Mostafazadeh, A. (Ali) |
|---|---|
| Imprint: | Huntington, N.Y. : Nova Science Publishers, c2001. |
| Description: | xv, 260 p. ; 26 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4594820 |
Table of Contents:
- Preface
- Acknowledgments
- Conventions and Notation
- 1. Quantum Mechanics of Nonconservative Systems
- 1.1. Basic Kinematic Structure
- 1.2. Basic Dynamical Structure I: The Schrodinger Picture
- 1.3. Basic Dynamical Structure II: The Heisenberg Picture
- 1.4. Basic Dynamical Structure III: Dynamics in the State Space
- 1.5. Schrodinger Equation for Periodic Hamiltonians
- 1.6. Comments and Bibliographical Notes
- 2. Algebraic Properties of Quantum Mechanics
- 2.1. Symmetry in Quantum Mechanics
- 2.2. Quantum Canonical Transformations
- 2.3. Kinematic and Dynamical Groups and Algebras
- 2.4. Comments and Bibliographical Notes
- 3. Dynamical Invariants
- 3.1. Dynamical Invariants and the Solution of the Schrodinger Equation
- 3.2. Symmetries of Invariants and Uniqueness of the Evolution Operator
- 3.3. Canonical Transformations of Dynamical Invariants
- 3.4. Dynamical Invariants for Systems Possessing a Dynamical Group
- 3.5. Comments and Bibliographical Notes
- 4. Quantum Adiabatic Approximation
- 4.1. Dynamical Invariants and Adiabatic Approximation
- 4.2. Adiabatic Dynamical Invariants
- 4.3. Adiabatic Series Expansion
- 4.4. Adiabatic Product Expansion
- 4.5. Comments and Bibliographical Notes
- 5. Cyclic and Noncyclic Geometric Phases
- 5.1. Adiabatic Evolution for a System with a Parametric Hamiltonian
- 5.2. Coordinate Transformations and Berry's Connection One-Form
- 5.3. Adiabatic Geometric Phase
- 5.4. Adiabatic Geometric Phase and Transition Amplitudes
- 5.5. Berry's Phase and Its non-Abelian Generalization
- 5.6. Nonadiabatic Geometric Phase
- 5.7. Cyclic Geometric Phase
- 5.8. Geometric Phase for Systems Possessing a Dynamical Group
- 5.9. Comments and Bibliographical Notes
- 6. Spin System
- 6.1. Hilbert Space for the Spin System
- 6.2. Eigenvalue Problem for the Spin Hamiltonian
- 6.3. Eigenvalue Problem for Dynamical Invariants
- 6.4. Solution of the Schrodinger Equation for the Spin System Using Dynamical Invariants
- 6.5. Adiabatic Approximation for the Spin System
- 6.6. Adiabatic Series and Product Expansions for the Spin System
- 6.7. Spin in a Precessing Magnetic Field
- 6.8. Abelian Geometric Phase for the Spin System
- 6.9. Non-Abelian Geometric Phase for the Spin System
- 6.10. Comments and Bibliographical Notes
- 7. Generalized Harmonic and Singular Oscillators
- 7.1. Hilbert Space of the Generalized Harmonic Oscillator
- 7.2. Eigenvalue Problem for the Generalized Harmonic Oscillator Hamiltonian
- 7.3. Solution of the Schrodinger Equation Using Dynamical Invariants
- 7.4. Solution of the Schrodinger Equation Using Canonical Transformations
- 7.5. Adiabatic Approximation for Generalized Harmonic Oscillator
- 7.6. Geometric Phase for Generalized Harmonic Oscillator
- 7.7. Linear Dynamical Invariants for Generalized Harmonic Oscillator
- 7.8. Generalized Singular Oscillator
- 7.9. Comments and Bibliographical Notes
- 8. Particle Confined between Moving Boundaries
- 8.1. Hilbert Space of a Particle Confined between Moving Boundaries
- 8.2. Transforming to Fixed Boundaries
- 8.3. Some Exactly Solvable Cases
- 8.4. Eigenvalue Problem for the Hamiltonian of a Free Particle Confined between Moving Boundaries
- 8.5. Adiabatic Evolution of a Free Particle Confined between Moving Boundaries
- 8.6. Adiabatic Geometric Phase due to Moving Boundaries
- 8.7. Comments and Bibliographical Notes
- Appendices
- A. Manifolds and Differential Forms
- A.1. Basic Properties of Manifolds
- A.2. Global Properties of Manifolds
- A.3. Tangent Vectors and Differential Forms
- A.4. Wedge Product and Exterior Derivative
- A.5. Integration on Manifolds
- B. Lie Groups and Lie Algebras
- B.1. Basic Properties of Lie Groups and Lie Algebras
- B.2. Lie Groups and Symmetries
- Bibliography
- Index
