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: aN Invalid Date NaN
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
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
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.
Keywords
Information
- Type
- Chapter
- Information
- Quantum MechanicsA Physical Approach, pp. 270 - 299Publisher: Cambridge University PressPrint publication year: 2025
- Creative Commons
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC 4.0 https://creativecommons.org/cclicenses/
Accessibility standard: Inaccessible, or known limited accessibility
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this book is known to have missing or limited accessibility features.
We may be reviewing its accessibility for future improvement, but final compliance is
not yet assured and may be subject to legal exceptions. If you have any questions,
please contact
accessibility@cambridge.org.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You have
Access
Open access