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Operator methods in quantum mechanics /
Operator Methods in Quantum Mechanics.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
North Holland,
�1981.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Operator Methods in Quantum Mechanics; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; A Message to the Reader; List of Symbols; Chapter 1. One-Dimensional Motion; 1.1. Position; 1.2. Mathematical Expectation; 1.3. Momentum; 1.4. Energy; 1.5. Observables; 1.6. Operators; 1.7. Functions of Observables; 1.8. Self-Adjoint Operators; 1.9. Hilbert Space; 1.10. The Spectral Theorem; Exercises; Chapter 2. The Spectrum; 2.1. The Resolvent; 2.2. Finding the Spectrum; 2.3. The Position Operator; 2.4. The Momentum Operator; 2.5. The Energy Operator
- 2.6. The Potential2.7. A Class of Functions; 2.8. The Spectrum of H; Exercises; Chapter 3. The Essential Spectrum; 3.1. An Example; 3.2. A Calculation; 3.3. Finding the Eigenvalues; 3.4. The Domain of H; 3.5. Back to Hilbert Space; 3.6. Compact Operators; 3.7. Relative Compactness; 3.8. Proof of Theorem 3.7.5; Exercises; Chapter 4. The Negative Eigenvalues; 4.1. The Possibilities; 4.2. Forms Extensions; 4.3. The Remaining Proofs; 4.4. Negative Eigenvalues; 4.5. Existence of Bound States; 4.6. Existence of Infinitely Many Bound States; 4.7. Existence of Only a Finite Number of Bound States
- 4.8. Another CriterionExercises; Chapter 5. Estimating the Spectrum; 5.1. Introduction; 5.2. Some Crucial Lemmas; 5.3. A Lower Bound for the Spectrum; 5.4. Lower Bounds for the Essential Spectrum; 5.5. An Inequality; 5.6. Bilinear Forms; 5.7. Intervals Containing the Essential Spectrum; 5.8. Coincidence of the Essential Spectrum with an Interval; 5.9. The Harmonic Oscillator; 5.10. The Morse Potential; Exercises; Chapter 6. Scattering Theory; 6.1. Time Dependence; 6.2. Scattering States; 6.3. Properties of the Wave Operators; 6.4. The Domains of the Wave Operators; 6.5. Local Singularities
- ExercisesChapter 7. Long-Range Potentials; 7.1. The Coulomb Potential; 7.2. Some Examples; 7.3. The Estimates; 7.4. The Derivatives of V(x); 7.5. The Relationship Between Xt and V(x); 7.6. An Identity; 7.7. The Reduction; 7.8. Mollifiers; Exercises; Chapter 8. Time-Independent Theory; 8.1. The Resolvent Method; 8.2. The Theory; 8.3. A Simple Criterion; 8.4. The Application; Exercises; Chapter 9. Completeness; 9.1. Definition; 9.2. The Abstract Theory; 9.3. Some Identities; 9.4. Another Form; 9.5. The Unperturbed Resolvent Operator; 9.6. The Perturbed Operator; 9.7. Compact Operators
- 9.8. Analytic Dependence9.9. Projections; 9.10. An Analytic Function Theorem; 9.11. The Combined Results; 9.12. Absolute Continuity; 9.13. The Intertwining Relations; 9.14. The Application; Exercises; Chapter 10. Strong Completeness; 10.1. The More Difficult Problem; 10.2. The Abstract Theory; 10.3. The Technique; 10.4. Verification for the Hamiltonian; 10.5. An Extension; 10.6. The Principle of Limiting Absorption; Exercises; Chapter 11. Oscillating Potentials; 11.1. A Surprise; 11.2. The Hamiltonian; 11.3. The Estimates; 11.4. A Variation; 11.5. Examples; Exercises