Co' (20), 11 = 1
00 V 3
and
Co' (20), 02 =
16
With the required coefficients provided above the value of- P' -T' for m^ = (20)
can be expressed (by Eq. 9.26) as
1
-P(20)'-I'l -4- (2P(O())- )+ 4 (2P( )) )
16 16
+(2P(0 I (1e1))- 1)q(2P(1 (11))- 1) Eq. 9.29
Then, since P(0 1 11)+P(1 I 11)= 1 => (2P(1 I 11)- 1) =-(2P(0 1 1)-1), Eq. 9.29 simpli-
fies to
11 12
-|P(20)' -I' 4 -(2P(O 1(11)) 1)- 4 (2P( 1 (11))-1)2
=- [1+(2P(o0 I(11))- ( 1)]2 Eq. 9.30
4
=-P(0[ 11)2.
From the symmetry inherent in the problem, it follows that the m^ = (02) counter-
part of Eq. 9.30 is
-I P(02)' 'I = -P( 1 11)2, Eq. 9.31
and employing Eq. 9.30-31 with Proposition 7.5 yields (for the two-operator case)