Clebsch Gordan
Quantum Mechanics · Part 5
227 KB9 sections4 key equationsLaTeX typeset
Table of Contents
- 1.Definition
- 2.Selection Rules and Properties
- 3.Special Cases and Formulas
- 4.Example: Two Spin-1/2 ()
- 5.Tabulated Values
- 6.3j Symbols (Wigner 3j)
- 7.Applications in Matrix Elements
- 8.Computational Methods
- 9.Physical Examples
Key Equations
$$C_{m_1,m_2,m}^{j_1,j_2,j} = \langle j_1, m_1; j_2, m_2 | j_1, j_2; j, m \rangle$$
$$|j_1 - j_2| \leq j \leq j_1 + j_2$$
$$\sum_{j,m} C_{m_1,m_2,m}^{j_1,j_2,j} C_{m_1',m_2',m}^{j_1,j_2,j} = \delta_{m_1 m_1'}\delta_{m_2 m_2'}$$
$$C_{m,0,m}^{j,1,j} = \frac{m}{\sqrt{j(j+1)}}$$
Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.
Course Context
This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...
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