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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
      • allowed_projections()
      • allowed_canonical_3j_arguments()
      • allowed_canonical_6j_arguments()
      • allowed_canonical_9j_arguments()
      • allowed_canonical_12j_first_arguments()
      • allowed_canonical_12j_second_arguments()
      • allowed_couplings()
      • allowed_couplings_12()
      • allowed_couplings_13()
      • allowed_couplings_23()
      • clebsch_gordan()
      • gaunt()
      • racah_w()
      • recoupling_12_23()
      • recoupling_12_13()
      • recoupling_13_23()
      • recoupling()
      • valid_spin_state()
      • triangle_condition()
      • spherical_harmonic()
      • spherical_harmonic()
      • triangle_coefficient()
      • wigner_12j_first()
      • wigner_12j_second()
      • wigner_3j()
      • wigner_3j()
      • wigner_6j()
      • wigner_6j()
      • wigner_9j()
      • wigner_9j()
      • wigner_d()
      • wigner_D()
      • character()
      • wigner::wigner_12j_first_args
      • wigner::wigner_12j_second_args
      • wigner::wigner_3j_args
      • wigner::wigner_6j_args
      • wigner::wigner_9j_args
  • 10. License
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© Copyright 2026, Andrew W. Jackura.

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