Re: addition of three angular momenta

*To*: mathgroup at smc.vnet.net*Subject*: [mg47749] Re: [mg47735] addition of three angular momenta*From*: Hugh Walker <hwalker at gvtc.com>*Date*: Sun, 25 Apr 2004 05:13:21 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On Saturday, April 24, 2004, at 03:15 AM, Francesco Siano wrote: > I am trying to use ClebschGordan[...] to generate the table of > coefficients for the addition of three or more angular momenta. > For the addition of two angular momenta J=J1+J2 I can do > > Table[ClebschGordan[{J1, m1}, {J2, m2}, {J, m}], {J, J1 + J2, Abs[J1 - > J2], -1}, {m, J, -J, -1}, {m1, J1, -J1, -1}, {m2, J2, -J2, -1}] > > For more than two angular momenta, J=J1+J2+J3 I should first add J1 and > J2, and then, for any Jtemp=J1+J2,J1+J2-1,...,Abs[J1-J2] add Jtemp and > J3 > and so on. > Any help would be greatly appreciated. > -Francesco Francesco, here is a notebook containing the basic functions for spin coupling. I have the same functions in package format which I can email upon request. Regards... ========== (* SpinCoupling[X_,Y_][j1_,j2_][J_,M_] uses the coefficients defined by ClebschGordan[{j1,m1},{j2,m2},{J,M}] functions to couple particles X and Y with spins j1 and j2, respectively, to give the coupled states j1+j2, j1+j2-1, j1+j2-2, ... Abs[j1-j2] according to quantum laws. SpinCoupling[X_,Y_,Z_][j1_,j2_][j12_,j3_][J_,M_] couples j1 and j2 to result in j12, which is then coupled to j3. *) (* Turn off ClebschGordan warnings *) Off[ClebschGordan::phy] (* Spin Coupling functions *) SpinCoupling[X_, Y_][j1_, j2_][J_, M_] := Sum[X[j1, m1]*Y[j2, m2]*ClebschGordan[{j1, m1}, {j2, m2}, {J, M}], {m2, j2, -j2, -1}, {m1, j1, -j1, -1}] SpinCoupling[X_, Y_, Z_][j1_, j2_][j12_, j3_][J_, M_] := ExpandAll[SpinCoupling[SpinCoupling[X, Y][j1, j2], Z][j12, j3][J, M]] ========== Hugh Walker Gnarly Oaks