Re: Wigner matrices Dpq(a) implementation
- To: mathgroup at smc.vnet.net
- Subject: [mg15943] Re: Wigner matrices Dpq(a) implementation
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 17 Feb 1999 23:34:07 -0500
- Organization: University of Western Australia
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Roberto Pratolongo wrote:
> I'm studying a branch of molecular dynamics, so I need to be familiar
> with rotating reference systems, and so son. Spherical harmonics are
> standard in Math, I know,and I've found the additional package about 3D
> rotation, but I also need to work with so-called Wigner matrices
> Dpq(a), that are a sort of spherical tensors of rank a=1,2,...
> I'm novice with the argument, but they have almost nothing to do with
> Wigner's 3J Symbol ,page 730 of Math3 manual, I suspect.
There are very important inter-relationships.
> Has anybody a reference for a suitable implementation of them.
I personally like
A R Edmonds, "Angular Momentum in Quantum Mechanics", Princeton
University Press, 1974.
Implementing them is straightforward using the definition (4.1.23) of
In:= d[m_, n_][j_][x_] = Sqrt[((j + m)! (j - m)!)/
((j + n)! (j - n)!)] Cos[x/2]^(m + n) Sin[x/2]^(m - n)*
JacobiP[j - m, m - n, m + n, Cos[x]];
In:= FullSimplify[d[1, 1][x]]
-- (9 Cos[x] + 2 Cos[2 x] + 7 (Cos[3 x] + 2 Cos[4 x]))
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA 6907 mailto:paul at physics.uwa.edu.au
God IS a weakly left-handed dice player
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