I2

5. The evolution of the spin in NMR ' An atom with spin % and magnetic moment p. = '73 is placed in a time dependent magnetic eld, tuned for resonance, B(t) = Boz + 81 (x cos wot y sin wot) , 0J0 = 730. Use the general solution for the evolution of a spin state, as given in lecture, to answer the following questions. (a) Assuming that initially the spin points in the positive zdirection, |(O)) = |+), give |(t)) and describe it as a spin pointing in a timedependent direction n(t) dened by timedependent angles 90:) and 9.303) that you should determine. (b) Use your answer above to eliminate t and write 96 as a function of 9. Where does the spin point as it lies, for the rst time, along the (at, y)plane