9j Symbol Calculator

The 9j symbol is related to the coupling probability for four angular momenta.

It is valid when

• j_i ≥ 0
• | j₁ - j₂ | ≤ j₃ ≤ j₁ + j₂ ("triangle relations")
• | j₄ - j₅ | ≤ j₆ ≤ j₄ + j₅
• | j₇ - j₈ | ≤ j₉ ≤ j₇ + j₈
• | j₁ - j₄ | ≤ j₇ ≤ j₁ + j₄
• | j₂ - j₅ | ≤ j₈ ≤ j₂ + j₅
• | j₃ - j₆ | ≤ j₉ ≤ j₃ + j₆

See any quantum physics textbook for details.

Download the standalone Java archive & source code (96 kb), distributed under the Apache License, Version 2.0.

If you find this calculator useful, please send me a postcard from your city:
Sven Gato Redsun, PO Box 1005, Santa Fe, NM 87504, USA

See also my 3j Symbol and 6j Symbol Calculators.