SixJSymbol

SixJSymbol[{j1,j2,j3},{j4,j5,j6}]

gives the values of the Wigner 6‐j symbol.

Details

  • The 6‐j symbols vanish except when certain triples of the j_(i) satisfy triangle inequalities.
  • The parameters of SixJSymbol can be integers, half‐integers, or symbolic expressions.

Examples

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Basic Examples  (2)

Evaluate a 6‐ symbol with integer arguments:

Use symbolic arguments to obtain exact symbolic answers:

Scope  (2)

SixJSymbol works with integer and half‐integer arguments:

TraditionalForm formatting:

Applications  (2)

Plot the 6‐j symbol as a function of j_(1) and j_(2):

Confirm the Wigner formula for the asymptotic value of SixJSymbol:

Properties & Relations  (2)

Generate a 6-j symbol from a generating function:

Express 6‐j symbols in terms of Clebsch–Gordan coefficients:

Possible Issues  (1)

A message is issued and the result 0 returned for unphysical cases:

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

Text

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

CMS

Wolfram Language. 1991. "SixJSymbol." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SixJSymbol.html.

APA

Wolfram Language. (1991). SixJSymbol. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SixJSymbol.html

BibTeX

@misc{reference.wolfram_2025_sixjsymbol, author="Wolfram Research", title="{SixJSymbol}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/SixJSymbol.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_sixjsymbol, organization={Wolfram Research}, title={SixJSymbol}, year={1991}, url={https://reference.wolfram.com/language/ref/SixJSymbol.html}, note=[Accessed: 21-February-2025 ]}