Chemistry Reference
In-Depth Information
ψ
1
=
a
i
Η
∧
ε
i
,
μ
i
α
ψ
0
=
a
0
Figure 10.1 Dipole transition between
c
0
and
c
1
for ground-state H
transition moment
m
i
from state
c
0
to
c
1
and its related excitation energy
«
ð>
0
Þ
as
i
m
2
i
2
a ¼
ð
10
:
21
Þ
«
i
In the uniform external field F, the atom acquires the potential energy
H
1
¼
Fz
ð
10
:
22
Þ
l
¼
F is nowa physical
perturbation parameter which can be acted upon from the laboratory
(e.g. by swithching on/off a plane condenser).
A simple Ritz variational calculation involving
whichwill be taken as the first-order perturbation.
c
1
, both states
being assumed normalized and orthogonal to each other, shows that the
energy of the atom in the field is lowered by the amount
c
0
and
D
E
¼
jhc
0
j
H
1
jc
1
ij
2
2
¼
F
2
ðc
0
c
1
j
z
Þ
«
«
i
i
!
F
2
ð
10
:
23
Þ
2
i
2
i
¼
F
2
m
1
2
2
m
1
2
a
F
2
i
¼
¼
«
«
i
can be obtained as the negative of
the second derivative of the energy with respect to the field F evaluated
at F
¼
0:
From this relation follows that
a
!
d
2
D
E
dF
2
a ¼
ð
10
:
24
Þ
F
¼
0
Turning to our perturbation theory, we take
1
2
r
1
r
H
¼
H
0
Fz
;
H
0
¼
2
ð
10
:
25
Þ
