ClebschGordan [{j1,m1},{j2,m2},{j,m}]
gives the Clebsch–Gordan coefficient for the decomposition of in terms of .
ClebschGordan
ClebschGordan [{j1,m1},{j2,m2},{j,m}]
gives the Clebsch–Gordan coefficient for the decomposition of in terms of .
Details
- The Clebsch–Gordan coefficients vanish except when and the satisfy a triangle inequality.
- The parameters of ClebschGordan can be integers, half‐integers, or symbolic expressions.
- The Wolfram Language uses the standard conventions of Edmonds for the phase of the Clebsch–Gordan coefficients.
- The Clebsch–Gordan coefficients and 3‐ symbols in the Wolfram Language satisfy the relation .
Examples
open all close allBasic Examples (2)
Evaluate a Clebsch–Gordan coefficient with integer arguments:
Use symbolic arguments to obtain exact symbolic answers:
Scope (2)
ClebschGordan works with integer and half‐integer arguments:
For symbolic input ClebschGordan evaluates to ThreeJSymbol :
Applications (3)
Plot Clebsch–Gordan coefficients as a function of and :
Decompose a spherical harmonic into a sum of products of two spherical harmonics:
Apply angular momentum operators to spherical harmonics:
Properties & Relations (2)
Evaluate the completely symbolic case of ClebschGordan :
Demonstrate ‐sum orthogonality:
Possible Issues (1)
A message is issued and the result of 0 is returned when :
Neat Examples (1)
Visualize contours constructed from Clebsch–Gordan coefficients:
See Also
Related Guides
Related Links
History
Introduced in 1991 (2.0)
Text
Wolfram Research (1991), ClebschGordan, Wolfram Language function, https://reference.wolfram.com/language/ref/ClebschGordan.html.
CMS
Wolfram Language. 1991. "ClebschGordan." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ClebschGordan.html.
APA
Wolfram Language. (1991). ClebschGordan. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ClebschGordan.html
BibTeX
@misc{reference.wolfram_2025_clebschgordan, author="Wolfram Research", title="{ClebschGordan}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/ClebschGordan.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_clebschgordan, organization={Wolfram Research}, title={ClebschGordan}, year={1991}, url={https://reference.wolfram.com/language/ref/ClebschGordan.html}, note=[Accessed: 16-November-2025]}