Chemistry Reference
In-Depth Information
α
,
M
s
= 1/2
S
+
S
-
β
,
M
s
= -1/2
S
= 1/2
The two-step ladder for spin
2
Figure 5.1
using Equations 5.17 twice it is easily seen that
3
4
a;
3
4
b
2
2
S
S
a ¼
b ¼
ð
5
:
19
Þ
so that the two spin states
a
and
b
have the same eigenvalue with respect
2
to the operator S
1
(S(S
þ
1) with S
¼
2
, doublet) and opposite eigen-
2
) with respect to S
z
. The name doublet (two
independent spin functions) comes from the so-called spin multiplicity
2S
þ
1.
1
2
1
value (M
S
¼
;
M
S
¼
5.3 THE DIRAC FORMULA FOR N-ELECTRON SPIN
For N
¼
2 electrons, we can write the 2
2
¼
4 products of two-electron
spin functions (which are already eigenfunctions of the operator S
z
):
aa; ab; ba; bb
M
S
¼
100
1
ð
5
:
20
Þ
where electron labels are always assumed in dictionary order, namely:
a
1
a
2
; a
1
b
2
; b
1
a
2
; b
1
b
2
ð
5
:
21
Þ
and, therefore, are omitted for brevity.
