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36  1
5.73
Lecture
#36
updated September 19,
NEXT TIME
:e
–
in solids
(CTDL, pages 11561168)
LAST TIME
:
TODAY
:
Landé interval rule (assignment!)
ζζ
NLS
n
,,
()
↔
l
examples
evaluate matrix elements in Slater determinantal basis and in
manye
–
NJLSM
J
⟩
or NLM
L
SM
S
⟩
basis
1. electrons vs. holes—a shortcut:
(holes are a convenience in spectra of isolated atoms and
molecules, but they are an essential part of the
interpretive picture for solids)
2. Hund’s 3rd rule
3. Zeeman effect:
Landé gfactor formula via WE Theorem
(done previously by projection theorem)
4. Matrix elements of
H
Zeeman
in Slater determinantal basis
set.
No difference between electron and hole as far as
Zeeman effect is concerned.
er
ij
2
vs.
SO
H
Hs
L
S
s
SO
(one
for each L  S term)
(one
for entire configuration)
=
⋅→
⋅
→⋅
∑
∑
i
iii
i
n
ii
ar
l
l
l
off  diagonal
J = 0 intraconfigurational
matrix elements:
See notes [page 35 9]!
SO
∆
=
H
H
eg
I
H
SO
..
?
1
6
3
6
Read CTDL, pp. 11561178
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View Full Document36  2
5.73
Lecture
#36
updated September 19,
1.
relationship between configurations with N e
–
vs. N “holes”
for p
5
is it necessary to consider all 5 e
–
?
is the sign flip just a coincidence?
NO!
TRICK:
Hole is exactly equivalent to e
–
(for identical LM
L
SM
S
or JLSM
J
)
except that the sign of its charge is reversed.
* no effect on e
2
/r
ij
because 2 interacting particles have charge of the
same sign (either both e
–
or both hole), so e
2
/r
ij
is always a
repulsive interaction
.
[What happens for f
13
p?
Certainly different
from fp!]
*
reverse sign for
H
SO
because
H
SO
is a relativistic electrostatic
interaction between e
–
and nucleus (+ charge).
Replacing e
–
by h
+
and leaving the sign on the nucleus the same reverses the sign of
H
SO
!
subshell
1/ 2 full subshell
s
p d f
# e
1
3 5 7
n
N
l
()
−
e.g.
1 1 0 0
1
(±1 is the unoccupied spin  orbital.
It is the "hole")
1100 1
αβαβ
α
β
ζα
β
α
β
α
ζ
−=
=
=
===
−
=−
+−
−
∑
−
np
P M
M
np
P M
M
e
LS
SO
n
p
i
iz
iz
np
52
2
11
2
2
1
2
1
2
00
1
2
5
,
/
,
/
H
ls
h
so expectation value of
SO
SO
H
H
:
,
/
5
1
2
2
1
1
1
2
2
12
2
e
np
P M
M
e
np
n
p
z
z
np
−
−
=+
ζ
ζ
h
s
l
h
but for single e
–
(with
the
same
M
L
, M
S
as
the five e
–
)
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 Spring '04
 RobertField

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