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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 Î-́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 α4; 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
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 Î-́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 α4; 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