(* Oliver Schedletzky, Burkhard Luy and Steffen J. Glaser, Analytical Polarization and Coherence Transfer Functions for Three Coupled Spins 1/2 under Planar Mixing Conditions Journal of Magnetic Resonance 130, 27-32 (1998). A Hamiltonian of the form H=2 pi J (I1xI2x + I1yI2y) is assumed (expanded to 3 spins, of course). The effective planar couplings between spins 1 and 2 is called j12 etc.. The coupling constants have to be defined right after the Clear command below. The variable transfer12 will give the polarization transfer function for I1z -> I2z under the above mentioned Hamiltonian. Correspondingly transfer13 or transfer11 corresponds to I1z -> I3z and I1z -> I1z, respectively. Transfer functions to zero quantum operators should be clear from the name given (e.g. transfer11y2z corresponds to the coherence transfer function I1z -> I1yI2z). Please cite the above mentioned reference whenever you use this program for scientific work. *) Clear[j12,j13,j23,x1,x2,x3,y1,y2,y3,z1,z2,z3,v1,v2,v3,w1,w2,w3, n1,n2,n3,c1,c3,lamb1,lamb2,lamb3,delta12,delta13,delta23, h, phi,s,p] j23=11 j12=-10 j13=4.6 a12=(1/(2 n1^2 n2^2)) ((x1 x2-y1 y2)^2 - (z1 z2)^2) a13=(1/(2 n1^2 n3^2)) ((x1 x3-y1 y3)^2 - (z1 z3)^2) a23=(1/(2 n2^2 n3^2)) ((x2 x3-y2 y3)^2 - (z2 z3)^2) w12=x1 x2-y1 y2-z1 z2 w13=x1 x3-y1 y3-z1 z3 w23=x2 x3-y2 y3-z2 z3 v12=(1/(2 n1^2 n2^2)) v13=(1/(2 n1^2 n3^2)) v23=(1/(2 n2^2 n3^2)) n1=Sqrt[x1^2 + y1^2 + z1^2] n2=Sqrt[x2^2 + y2^2 + z2^2] n3=Sqrt[x3^2 + y3^2 + z3^2] x1=-j12*j23/4-j13*lamb1/(Pi 2)/2 x2=-j12*j23/4-j13*lamb2/(Pi 2)/2 x3=-j12*j23/4-j13*lamb3/(Pi 2)/2 y1=-j12*j13/4-j23*lamb1/(Pi 2)/2 y2=-j12*j13/4-j23*lamb2/(Pi 2)/2 y3=-j12*j13/4-j23*lamb3/(Pi 2)/2 z1=j12^2/4-(lamb1/(Pi 2))^2 z2=j12^2/4-(lamb2/(Pi 2))^2 z3=j12^2/4-(lamb3/(Pi 2))^2 no1={N[x1/n1],N[y1/n1],N[z1/n1]} no2={N[x2/n2],N[y2/n2],N[z2/n2]} no3={N[x3/n3],N[y3/n3],N[z3/n3]} delta12=lamb1-lamb2 delta13=lamb1-lamb3 delta23=lamb2-lamb3 lamb1=2 Pi h Cos[phi/3] lamb2=-2 Pi h Cos[(Pi-phi)/3] lamb3=-2 Pi h Cos[(Pi+phi)/3] phi=ArcCos[Abs[p]/(s^3)] h=(Abs[p]/p) s s=Sqrt[(j12^2 + j13^2 + j23^2)/3] p=j12 j13 j23 com1=a12(1-Cos[delta12 t]) com2=a13(1-Cos[delta13 t]) com3=a23(1-Cos[delta23 t]) transfer11=N[1-(v12 w12^2 (1-Cos[delta12 t]) +v13 w13^2 (1-Cos[delta13 t]) +v23 w23^2 (1-Cos[delta23 t]))] transfer12= N[(a12(1-Cos[delta12 t]) +a13(1-Cos[delta13 t]) +a23(1-Cos[delta23 t]))] transfer13= N[v12 ((x1 x2-z1 z2)^2-(y1 y2)^2)(1-Cos[delta12 t]) +v13 ((x1 x3-z1 z3)^2-(y1 y3)^2)(1-Cos[delta13 t]) +v23 ((x2 x3-z2 z3)^2-(y2 y3)^2)(1-Cos[delta23 t])] transfer11x2y=N[v12 w12 (y1 x2-x1 y2) Sin[delta12 t] +v13 w13 (y1 x3-x1 y3) Sin[delta13 t] +v23 w23 (y2 x3-x2 y3) Sin[delta23 t]] transfer11x3y=N[v12 w12 (z1 x2-x1 z2) Sin[delta12 t] +v13 w13 (z1 x3-x1 z3) Sin[delta13 t] +v23 w23 (z2 x3-x2 z3) Sin[delta23 t]] transfer12x3y=N[v12 w12 (z1 y2-y1 z2) Sin[delta12 t] +v13 w13 (z1 y3-y1 z3) Sin[delta13 t] +v23 w23 (z2 y3-y2 z3) Sin[delta23 t]] transfer112323=N[v12 w12 (y1 z2+z1 y2) (1-Cos[delta12 t])/2 +v13 w13 (y1 z3+z1 y3) (1-Cos[delta13 t])/2 +v23 w23 (y2 z3+z2 y3) (1-Cos[delta23 t])/2] transfer121313=N[v12 w12 (x1 z2+z1 x2) (1-Cos[delta12 t])/2 +v13 w13 (x1 z3+z1 x3) (1-Cos[delta13 t])/2 +v23 w23 (x2 z3+z2 x3) (1-Cos[delta23 t])/2] transfer131212=N[v12 w12 (x1 y2+y1 x2) (1-Cos[delta12 t])/2 +v13 w13 (x1 y3+y1 x3) (1-Cos[delta13 t])/2 +v23 w23 (x2 y3+y2 x3) (1-Cos[delta23 t])/2]