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Quantum mechanics and electrodynamics /
This book highlights the power and elegance of algebraic methods of solving problems in quantum mechanics. It shows that symmetries not only provide elegant solutions to problems that can be solved exactly, but also substantially simplify problems that must be solved approximately. Furthermore, the...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Printed Book |
| Language: | English Czech |
| Subjects: | |
| Online Access: | SpringerLink - Full text online |
Table of Contents:
- Preface; A Few Words of Explanation; Prerequisites; Acknowledgments; Errors; Contents; List of Exercises; Notation, Convention, Units, and Experimental Data; Notation; The Summation Convention; The Component Formalism; Units; Fundamental Constants; Experimental Data; References; 1 Foundations of Quantum Mechanics; 1.1 Basic Principles; 1.2 Mathematical Scheme of the Quantum Theory; 1.2.1 Stern-Gerlach Experiments; 1.2.2 Operators; 1.2.3 Time Evolution in Quantum Theory; 1.2.4 Stationary States.
- 1.2.5 Properties of Hermitian Operators1.2.6 Ambiguity in the Determination of States; 1.2.7 Rabi Method of Magnetic Moments; 1.3 Systems with More Degrees of Freedom; 1.3.1 Expected Values of Operators and Their Time Evolution; 1.3.2 Canonical Quantization; 1.3.3 Harmonic Oscillator; 1.3.4 Abstract Solution; 1.3.5 Matrix Representation; 1.3.6 Dirac �I�-Function; 1.3.7 Coordinate Representation; 1.3.8 Momentum Representation; 1.3.9 Gaussian Packet and the Uncertainty Principle; 1.4 Final Notes; References.
- 2 Approximate Methods in Quantum Mechanics2.1 Variational Method; 2.1.1 The Ritz Variational Principle; 2.1.2 Optimization of Nonlinear Parameters; 2.1.3 Optimization of Linear Parameters; 2.2 Perturbation Method; 2.2.1 Isolated Levels; 2.2.2 Degenerate Levels; 2.2.3 Note on the Error of the Perturbation Method; References; 3 The Hydrogen Atom and Structure of Its Spectral Lines; 3.1 A Particle in an Electromagnetic Field; 3.2 The Gross Structure; 3.2.1 The Problem of Two Particles; 3.2.2 Electrostatic Potential; 3.2.3 Units.
- 3.2.4 Spherical Coordinates3.2.5 Solution for s-States; 3.2.6 Comparison with Experiment; 3.3 The Hyperfine Structure; 3.3.1 Magnetic Field of a Dipole; 3.3.2 Hamiltonian of a Particle with Spin in an External Electromagnetic Field; 3.3.3 Hyperfine Splitting of the Hydrogen Ground State; 3.3.4 Classification of States Using the Integrals of Motion; 3.4 Orbital Angular Momentum; 3.4.1 Significance of Angular Momentum; 3.4.2 Angular Dependence of p-States; 3.4.3 Accidental Degeneracy; 3.5 Fine Structure; 3.5.1 Relativistic Corrections.
- 3.5.2 Fine Splitting of the Energy Level n = 23.5.3 Classification of States Using the Integrals of Motion; 3.6 Hamiltonian of Two Particles with Precision to �I�4; 3.6.1 Magnetic Field of a Moving Charge; 3.6.2 Hamiltonian of Two Particles in an External Electromagnetic Field; 3.6.3 Helium-Like Atoms; 3.6.4 Hydrogen-Like Atoms; 3.6.5 Final Notes; References; 4 Treasures Hidden in Commutators; 4.1 A General Solution To Angular Momentum; 4.2 Addition of Angular Momenta; 4.3 The Runge-Lenz Vector.