Wigner3j.m

Wigner3j(j1,j2,j,m1,m2,m) returns the Wigner 3j-symbol.

Description

Wigner3j(j1,j2,j,m1,m2,m) returns the Wigner 3j-symbol, where j1, j2, j, m1, m2, and m are half-integers. Physically, the Wigner 3j-symbol is closely related to the Clebsch-Gordon coefficient <j1,j2,m1,m2|j1,j2,j,m>, the square of which is the probability that a system of two particles with angular momentum j1 and j2 respectively and z-component of angular momentum m1 and m2 respectively has total angular momentum j and z-component of total angular momentum m.

I haven't tested this function thoroughly yet, so there may be some bugs. Please let me know if you find any.

• Acknowledgements: This submission has inspired the following:; Wigner3j symbol
• MATLAB release: MATLAB 6.0 (R12)

[Kobi Kraus]

The loop in rows 59-64 can be replaced by a simple direct sum:
t = tmin : tmax;
wigner = sum( (-1).^t ./ ( factorial(t) .* factorial(t-t1) .* factorial(t-t2) ...
                .* factorial(t3-t) .* factorial(t4-t) .* factorial(t5-t) ) );

[Lisa de Groot]

The file does not check wether the condition m1 + m2 = m3 is fulfilled. This should be added.

[Brice DUBOST]

 

[Brice DUBOST]

It doesn't respect wigner 3j symetries

Wigner3j(1,1,1,1,-1,-1) is not 0

[Par Hakansson]

Made quick test against alpha=beta=gamma=0 3jsymbols in Table 2, in D.M. Brink and R.G. Satchler "Angular Momentum" Oxford Science Publications and can not get a match

[Par Hakansson]

Ops, did not read the table caption, it was 3jsymbol squared in table. now it match better for a few test cases

[Christian Mueller]

Still, the file does not check if the condition m1 + m2 = m3 is fulfilled. This should still be added!! In the current version it's very problematic to use the code! False results e.g. for angular momentum couplings are inevitable with this code.