QMGreensite_merged

The wavefunctions of [2.158] are symmetric or antisymmetric under
the exchange of identical particles, as is required by the postulates of
quantum mechanics ( 5 ). The energies of the four eigenstates are

E 1 ¼^12 !Iþ^12 !Sþ^12 JIS, E 2 ¼D
^12 JIS,

E 3 ¼
D
^12 JIS, E 4 ¼
^12 !I
^12 !Sþ^12 JIS,

½ 2 : 159 Š

where

D¼

1

2

ðÞ!I
!S^2 þðÞ 2 JIS^2

    1 = 2

: ½ 2 : 160 Š

In the strongly coupled spectrum, the energies of the stationary
states and the positions of the resonance signals in the spectrum are
altered, compared to the weakly coupled spin system (see [1.56]).
In addition, the intensities of the lines in the multiplet are no longer
of equal intensity; specifically, the two outer lines reduce progres-
sively in intensity as the strong coupling effect becomes more
pronounced.
The results given in [2.156]–[2.160] are derived by diagonalizing
the Hamiltonian matrix in the product basis; these results can be easily
verified. For example, if
2 is an eigenfunction ofH, then

H
 2 ¼E 2 
 2

¼ðÞ!IIzþ!SSzþ 2 JISISðÞcosj iþsinj i

¼^12 !Icos


^12 !Isin


^12 !Scos

þ^12 !Ssin

^12 JIScos


^12 JISsin

þJIScos

þJISsin

¼^12 ðÞ!Icos
!Scos
JIScosþ 2 JISsin

þ^12 ðÞ
!Isinþ!Ssin
JISsinþ 2 JIScos

¼^12 ðÞ!I
!S
JISþ 2 JIStancos

þ^12 ðÞ
!Iþ!S
JISþ 2 JIS=tan sin

:

½ 2 : 161 Š

2.5 QUANTUMMECHANICS OFMULTISPINSYSTEMS 63