Book contents
- Frontmatter
- Contents
- Preface
- 1 The Quantum World and Its Description
- 2 Matter and Field
- 3 Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4 Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5 One-Dimensional Potential Steps, Barriers, and Wells
- 6 The WKB Approximation. Electronic Properties of Solids
- 7 The Free Particle. The Time-Dependent Schrödinger Equation
- 8 Dynamics of Quantum Systems
- 9 The One-Dimensional Harmonic Oscillator
- 10 The Physics Underlying Quantum Phenomena
- 11 Angular Momentum Theory
- 12 Central Potentials. The Hydrogen Atom
- 13 Stationary Perturbation Theory and the Variational Method
- 14 The Electron Spin. Entangled States
- 15 Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16 Atoms and Molecules
- 17 Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18 Elastic Scattering Theory
- 19 Relativistic Equations. An Introduction
- Appendix A Mathematical Tools
- References
- Index
11 - Angular Momentum Theory
Published online by Cambridge University Press: 27 December 2025
Book contents
- Frontmatter
- Contents
- Preface
- 1 The Quantum World and Its Description
- 2 Matter and Field
- 3 Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4 Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5 One-Dimensional Potential Steps, Barriers, and Wells
- 6 The WKB Approximation. Electronic Properties of Solids
- 7 The Free Particle. The Time-Dependent Schrödinger Equation
- 8 Dynamics of Quantum Systems
- 9 The One-Dimensional Harmonic Oscillator
- 10 The Physics Underlying Quantum Phenomena
- 11 Angular Momentum Theory
- 12 Central Potentials. The Hydrogen Atom
- 13 Stationary Perturbation Theory and the Variational Method
- 14 The Electron Spin. Entangled States
- 15 Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16 Atoms and Molecules
- 17 Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18 Elastic Scattering Theory
- 19 Relativistic Equations. An Introduction
- Appendix A Mathematical Tools
- References
- Index
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Summary
Chapter 11 is devoted to the quantum theory of angular momentum. As in classical mechanics, working with angular momentum requires leaving the one-dimensional space, with all the complications that this entails. The importance of angular momentum resides in at least three facts: i) central problems are of particular interest; (ii) many particles have an intrinsic angular momentum (the spin); and iii) the physics of angular momentum involves features such as the so-called space quantization. The first part of the chapter deals with the orbital angular momentum and its eigenfunctions, the spherical harmonics. Its algebraic properties, embodied in the matrix representation, allow for an extension of the theory to half-integer angular momentum in terms of Pauli matrices, as well as the addition of angular momenta.
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- Quantum MechanicsA Physical Approach, pp. 270 - 299Publisher: Cambridge University PressPrint publication year: 2025
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