(* Burkhard Luy, Oliver Schedletzkyi, and Steffen J. Glaser, Analytical Polarization Transfer Functions for Four Coupled Spins 1/2 under Isotropic Mixing Conditions Journal of Magnetic Resonance 138, 19-27 (1999). A Hamiltonian of the form H=2 pi J (I1xI2x + I1yI2y + I1zI2z) is assumed (expanded to 4 spins, of course). The scalar couplings between spins 1 and 2 is called j12 etc.. The coupling constants have to be defined right after this comment. The polarization transfer I1z -> I2z is stored in tr12 and the transfer I1z -> I2z is stored in tr11. Please cite the above mentioned reference whenever you use this program for scientific work. SPECIAL CASE OF AN AX3 SPIN SYSTEM *) (*Kopplungskonstanten *) J12=10 J13=j12 J14=j12 J23=0 J24=0 J34=0 (* Vorstufen *) (* Winkel *) (* lambda,mue,nues *) lambda0=j12 lambda1=-j12 lambda2=0 lambda3=-2 j12 d01=lambda0-lambda1 d02=lambda0-lambda2 d03=lambda0-lambda3 d12=lambda1-lambda2 d13=lambda1-lambda3 d23=lambda2-lambda3 (* Zur Eigenvektorbestimmung *) (* Vorstufen zu Vorfaktoren *) (* die Vorfaktoren *) a1= 1/4 a2= 5/16 (* Die Transferfunktion *) sum1=a1(1-Cos[(2 Pi J12)*tau])+a2(1-Cos[(4 Pi J12)*tau]) sum2=b12(1-Cos[(mue1-mue2)*tau])+b13(1-Cos[(mue1-mue3)*tau])+b23(1-Cos[(mue2-mue3)*tau]) sum3=c11(1-Cos[(mue1-nu1)*tau])+c12(1-Cos[(mue1-nu2)*tau])+ c21(1-Cos[(mue2-nu1)*tau])+c22(1-Cos[(mue2-nu2)*tau])+ c31(1-Cos[(mue3-nu1)*tau])+c32(1-Cos[(mue3-nu2)*tau]) transfer12=sum1 tr=Simplify[N[transfer12]] Plot[tr, {tau,0,0.256}]