Click or drag to resize

VectorCouplingClebschGordan Method

Calculates the Clebsch-Gordan coefficient using the relation to the Wigner 3-j symbol: l1-l2+m3 1/2 ( l1 l2 l3 ) (l1 m1 l2 m2 | l3 m3) = (-1) (2*l3+1) ( m1 m2 -m3 )

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)
Syntax
C#
Copy
public static double ClebschGordan(
	double l1,
	double m1,
	double l2,
	double m2,
	double l3,
	double m3,
	out int errflag
)

Parameters

l1  Double
Parameter in the 3j symbol.
m1  Double
Magnetic quantum number associated with l1.
l2  Double
Second angular-momentum parameter in the 3j symbol.
m2  Double
Magnetic quantum number associated with l2.
l3  Double
Third angular-momentum parameter in the 3j symbol.
m3  Double
Magnetic quantum number associated with l3.
errflag  Int32
Error flag.

errflag=0 No errors.

errflag=1 Either l1 < abs(m1) or l1+abs(m1) is non-integer.

errflag=2abs(l1-l2)<= l3 <= l1+l2 not satisfied.

errflag=3l1+l2+l3 is not an integer.

errflag=4m2max-m2min is not an integer.

errflag=5m2max is less than m2min.

errflag=6ndim is less than m2max-m2min+1.

errflag=7m1+m2-m3 is not zero.

Return Value

Double
The value of the Clebsch-Gordan coefficient.
Remarks
References: ----------- 1. See routines in "threejj.cc" and "threejm.cc" for references about the calculation of the Wigner 3-j symbols. 2. C++ Implementation for the Matpack C++ Numerics and Graphics Library by Berndt M. Gammel in June 1997. Note: ----- Whenever you have to calculate a series of Clebsch-Gordan coefficients for a range of l-values or m-values you should probably use the 3-j symbol routines. These calculate the 3-j symbols iteratively for a series of l-values or m-values and are therefore much more efficient. Use the relation between Clebsch-Gordan coefficients and Wigner 3-j symbols as given above.
See Also