in which and are the stationary states andE ¼h! andE ¼h!
are the energies of the states withm¼1/2 andm¼–1/2, respectively, and
a¼|a| exp[i a] andb¼|b| exp[i b] are complex numbers satisfying the
normalization relation |a|^2 þ|b|^2 ¼1. U sing [2.19] yields
hix ¼Z
xd ¼Z
Ixd ¼ aaZ
Ix d þ abexpið! ! Þt Z
Ix d þ abexpið! ! Þt Z
Ix d þ bbZ
Ix d ¼
hjajjbj
2
expifð! ! Þtþ g
þexpifð! ! Þtþ g ¼ hjajjbjcosð! ! Þtþ
¼ hjajjbjcos½! 0 tþ ,
½ 2 : 28 y
¼Z
yd ¼Z
Iyd ¼ aaZ
Iy d þ abexpið! ! Þt Z
Iy d þ abexpið! ! Þt Z
Iy d þ bbZ
Iy d ¼i
hjajjbj
2
expifð! ! Þtþ g
expifð! ! Þtþ g ¼ hjajjbjsinð! ! Þtþ
¼ hjajjbjsin½! 0 tþ ,
½ 2 : 29 hiz ¼Z
zd ¼Z
Izd ¼Z
aexpi! t
þbexpi! thi
Iz aexp½i! t þbexpi! t (^)
d
¼ aa
Z
Iz d þ abexpið! ! Þt
Z
Iz d
þ abexpið! ! Þt
Z
Iz d þ bb
Z
Iz d ,
¼
h
2
jaj^2 jbj^2
,
½ 2 : 30
36 CHAPTER 2 THEORETICALDESCRIPTION OFNMR SPECTROSCOPY