(* 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.
SPECIAL CASE J12=J13=J23
*)
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]
j12=10
a12=4/9
b12=4/9
b0=5/9
delta12=lamb1-lamb2
lamb1=2 Pi j12
lamb2=-Pi j12
transfer12= N[(a12*Sin[delta12/2 t]^2)]
transfer11= N[(b0+b12*Cos[delta12 t])]
Plot[transfer12, {t,0,1}]
Plot[transfer11, {t,0,1}]