ClebschGordan

ClebschGordan[{j1,m1},{j2,m2},{j,m}]

gives the ClebschGordan coefficient for the decomposition of in terms of .

Details

• The ClebschGordan coefficients vanish except when and the satisfy a triangle inequality.
• The parameters of ClebschGordan can be integers, halfintegers, or symbolic expressions.
• The Wolfram Language uses the standard conventions of Edmonds for the phase of the ClebschGordan coefficients.
• The ClebschGordan coefficients and 3 symbols in the Wolfram Language satisfy the relation .

Examples

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Basic Examples(2)

Evaluate a ClebschGordan coefficient with integer arguments:

Use symbolic arguments to obtain exact symbolic answers:

Scope(2)

ClebschGordan works with integer and halfinteger arguments:

For symbolic input ClebschGordan evaluates to ThreeJSymbol:

Applications(3)

Plot ClebschGordan 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 ClebschGordan coefficients:

Wolfram Research (1991), ClebschGordan, Wolfram Language function, https://reference.wolfram.com/language/ref/ClebschGordan.html.

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_2024_clebschgordan, author="Wolfram Research", title="{ClebschGordan}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/ClebschGordan.html}", note=[Accessed: 05-August-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_clebschgordan, organization={Wolfram Research}, title={ClebschGordan}, year={1991}, url={https://reference.wolfram.com/language/ref/ClebschGordan.html}, note=[Accessed: 05-August-2024 ]}