wigner

wigner is a C++23 static library for numerical SU(2) angular-momentum algebra. It provides the coupling, recoupling, rotation, and spherical-harmonic operations shared by spectrum and amplitude analyses.

The manual starts with a working program, then fixes conventions before describing each family of coefficients. Numerical limits, inspection tools, build and installation details, and the complete public API follow.

Contents

• 1. Overview and Quick Start
  • 1.1. Purpose
  • 1.2. Requirements
  • 1.3. Build and Test
  • 1.4. First Program
  • 1.5. Using Only What You Need
  • 1.6. Where to Continue
• 2. Conventions
  • 2.1. Doubled Quantum Numbers
  • 2.2. Orbital Exceptions
  • 2.3. Phase and Normalization
  • 2.4. Rotations
  • 2.5. Invalid Inputs and Mathematical Zeros
  • 2.6. Argument Order
• 3. Coupling and Recoupling Coefficients
  • 3.1. Selection Rules First
  • 3.2. Wigner 3j and Clebsch-Gordan
  • 3.3. Wigner 6j, Racah-W, and Recoupling
  • 3.4. Wigner 9j
  • 3.5. Wigner 12j
  • 3.6. Triangle Coefficient
  • 3.7. Choosing an Interface
• 4. Rotations and Spherical Harmonics
  • 4.1. Wigner d Matrices
  • 4.2. Wigner D Matrices
  • 4.3. SU(2) Characters
  • 4.4. Complex Spherical Harmonics
  • 4.5. Gaunt Coefficients
• 5. Selection Rules and Enumeration
  • 5.1. Basic Predicates
  • 5.2. Allowed Projections and Couplings
  • 5.3. Canonical Symbol Arguments
  • 5.4. Scaling Warning
  • 5.5. Ordering Guarantees
• 6. Numerical Design and Validation
  • 6.1. Floating-Point Policy
  • 6.2. Independent Reference Checks
  • 6.3. The 12j Boundary
  • 6.4. Failure Modes at Large j
  • 6.5. Reproducible Validation
• 7. Command-Line Tools
  • 7.1. Purpose
  • 7.2. Coupling and 3j Tools
  • 7.3. 6j and 9j Tools
  • 7.4. Recoupling Tool
  • 7.5. Rotations and Triangle Coefficients
  • 7.6. Reading Output Safely
• 8. Building and Integration
  • 8.1. Requirements
  • 8.2. Recommended Local Build
  • 8.3. Custom Build Directory
  • 8.4. Choosing a Compiler
  • 8.5. Manual CMake Build
  • 8.6. Installing Wigner
  • 8.7. Using an Installed Package
  • 8.8. Using Wigner as Source
  • 8.9. Documentation Targets
  • 8.10. CMake Options
  • 8.11. Version Compatibility
• 9. API Reference
  • wigner
• 10. License