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[ia] andb¼|b| exp[ib] are complex numbers satisfying the
normalization relation |a|^2 þ|b|^2 ¼1. U sing [2.19] yields
hix ¼
Z
xd¼
Z
Ixd
¼ aa
Z
Ix dþ abexpið! ! Þt
Z
Ix d
þ abexpið! ! Þt
Z
Ix dþ bb
Z
Ix d
¼
hjajjbj
2
expifð! ! Þtþg
þexpifð! ! Þtþg
¼ hjajjbjcosð! ! Þtþ
¼ hjajjbjcos½! 0 tþ,
½ 2 : 28
y
¼
Z
yd¼
Z
Iyd
¼ aa
Z
Iy dþ abexpið! ! Þt
Z
Iy d
þ abexpið! ! Þt
Z
Iy dþ bb
Z
Iy d
¼i
hjajjbj
2
expifð! ! Þtþg
expifð! ! Þtþg
¼ hjajjbjsinð! ! Þtþ
¼ hjajjbjsin½! 0 tþ,
½ 2 : 29
hiz ¼
Z
zd¼
Z
Izd
¼
Z
aexpi! t
þbexpi! t
hi
Iz
aexp½i! t þbexpi! t
(^)
d
¼ aa
Z
Iz dþ abexpið! ! Þt
Z
Iz d
þ abexpið! ! Þt
Z
Iz dþ bb
Z
Iz d,
¼
h
2
jaj^2 jbj^2
,
½ 2 : 30
36 CHAPTER 2 THEORETICALDESCRIPTION OFNMR SPECTROSCOPY