Elements of Modern Physics
304
a
a orientational
a ionic
a electronic
n
(a)
n
(b)
Absorption
Fig. 8.17 Schematic diagram illustrating the variation of
polarizability and absorption as a function of v.
Consider the behaviour of a bound electron in the presence of an
electromagnetic field E cos (ωt) in the z-direction. It was pointed out in Sec. 6.3,
that this introduces a potential
V = e E z cos ωt
(8.l26)
as a result of which the state changes to the expression in Eq. (6.41) with a m (t)
given by Eq. (6.48). The resulting dipole moment is given by
p = – e〈ψ(t) |z| ψ(t)〉
(8.127)
which on using Eqs. (6.41 and 6.48), after some analysis, gives, to leading
order in E
p ≈
2
2
0
0
0
1
1
cos
| |
ω
+
ω + ω ω − ω
∑
j
j
j
j
e E
t
z
(8.128)
where ω j0 = (E j – E 0 )/. From this, the polarizability is
α =
2
2
0
0
0
1
1
| |
+
ω + ω ω − ω
∑
j
j
j
j
e
z
(8.129)
It is observed that α takes sudden jumps whenever ω = (E j – E 0 )/. Also at
ω = (E j – E 0 )/, there are transitions to the state j, resulting in an absorption of
304
a
a orientational
a ionic
a electronic
n
(a)
n
(b)
Absorption
Fig. 8.17 Schematic diagram illustrating the variation of
polarizability and absorption as a function of v.
Consider the behaviour of a bound electron in the presence of an
electromagnetic field E cos (ωt) in the z-direction. It was pointed out in Sec. 6.3,
that this introduces a potential
V = e E z cos ωt
(8.l26)
as a result of which the state changes to the expression in Eq. (6.41) with a m (t)
given by Eq. (6.48). The resulting dipole moment is given by
p = – e〈ψ(t) |z| ψ(t)〉
(8.127)
which on using Eqs. (6.41 and 6.48), after some analysis, gives, to leading
order in E
p ≈
2
2
0
0
0
1
1
cos
| |
ω
+
ω + ω ω − ω
∑
j
j
j
j
e E
t
z
(8.128)
where ω j0 = (E j – E 0 )/. From this, the polarizability is
α =
2
2
0
0
0
1
1
| |
+
ω + ω ω − ω
∑
j
j
j
j
e
z
(8.129)
It is observed that α takes sudden jumps whenever ω = (E j – E 0 )/. Also at
ω = (E j – E 0 )/, there are transitions to the state j, resulting in an absorption of