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d
m
m
1
(0)
P+(x), P+ (x)
0.9
0.8
0.7
0
0.25
0.5 x
0.75
1
V(x) V0
x
V(x) G
a x V0
1
0.5
0
0.5
1
|A| /4 /0
2
1.5
0
50
100
150
200
ka
2 2
15 10
tan Ka Ka/a
5 0 5 10 15
0
1
2
3
4
5
6
7
8
Ka
1 0.8
F(t)
0.6 0.4 0.2 0
20
15
10
5
0
5
10
15
20
t
|kE
k |H 1 | i
j |H 1 | k
|i X
|j
V(x)
E
Intervalo perigoso
xo
x
V(x)
E
Intervalo perigoso
xo
x
E
0
x
V(x)
E
D+ D 0
C+ C x
V(x)
V(x)
E
I x1
II x2
III x
V(x)
E
I x1
II x2
III x
N=1 x2
x1 I II III
x
N=2
x1
x2
x
0
Aprox. harmonica
V(x) / V0
0.5
1 1 0.5 0 0.5 1
x/
V(x)
E V0 a x0 x
(a)1 r a
(b)1 r a
U(r)
U(r)
(c)1 r a
(d)1 r a
U(r)
U(r)
1
U(r)
a
r
l=0 ... n=4 n=3 n=2
l=1
l=2
l=3
...
E=0
n=1
1/2
+
+
+
+
+
+
+
# de estados
2
ms-1 / 2+ + + + + + +
1
mj = - 72
...
5 7 2 2
-3
0
3
1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 111111111 000000000 1111 0000 11111111111 00000000000 111111 000000 11111111111 00000000000 11 00 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 11111111111 00000000000 111111 000000 1 1111 0 0000 11111 1 00000 0 11 00 1 1111 111111111 0 0000 000000000 1 0 000 111 11 00 1 1111 111110011 0 0000 000001100 1 0 000 001100 111 110011 11 00
m
- 7 2
- 3 2
...
mj
3 2
7 2
H0
H0 + HLS2p3/2 R (1- 2/ 12) 4 R 4 R (1+ 2/ 6) 4
2s, 2p
R 4
2s1/2
2p1/2
H0 + HLS2p3/2 2s1/2 R (1- 2/ 12) 4 R 4 R (1+ 2/ 6) 4
+ HK
+ HD2p3/2
-7 R/ 192 2s1/2 2p1/2 -13 R/ 64 + R/ 82 2
2
2p1/2
H0
H 0+ HSS-R + E SS /4 E SS -R -3 E SS /4 S=0 S=1
-R
p2 e2 + r 2
+H E2 + | | ) | | 210
1 2
( 200
+
200 , 21m
E2
E2 E2 - | |
211 , 21-11 2
( 200
-
) | | 210
3000 2000 1000
++ 1 --
i (MHz)
0 -1000 -2000 -3000
20 1000 2000 3000
B (gauss)
u1
111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 3 u 111111111 000000000
u2
111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000u4 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000
V(r) r2
- e r
V(r)
2 - Ze r
|nlm l
Z=36
00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111
Kr
(6) (2) 4s
4p (10) 3d
Z=18
11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000
Ar
(6) (2) 3s
3p
Z=10
11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000
Ne
(6) (2) 2s
2p
Z= 2
00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11111111111111111111111111111111111111111111
He
(2)
1s
k1k -k
-k1 -k2
k2
k
1 0 11 00 1 00
11 00
p
111 000 1 0k
1k
1k
2 = 2
2
1 0 P
k
k
11 00 P
k
1 0 11 00 11 00p
11 00 11 00p
1 0
(a)Z p
k
1 0 11 00 11 00p
(b)
1 0 1 0 111 000 11 00k
1 0
I
11 00
1 0 11 00p
1 0
Z I
11 00 1 0p
Ze 4
1 0 1 0 1 0p
Ze
2
11 00 11 00 11 00p
11 00 11 00 11 00p
1 0 1 0
11 00 11 00
11 00 11 00 11 00p
En
nlm k
11 00 11 00nlm
E n
11 00 11 00 11 00 111 000 1 0 11 00k nlm
11 00 11 00
nlm
z
k
^ x ^ y
z
kx y
l=0 n=4 n=3 n=2x
l=1
l=2 n=3, l=0Pol. linear
n=2, l=1x
m=1 m=0 m=1 Pol. circular
n=1
^ 3
k
^ 1
^ 2
d d ^ x q u
q
q
^ u
3=3 3=3
2
1
O
2=2
1
1
2 1
5.37
2
+
5.17 5.11 4.77 3.59
2 2 2
+ + +
5.36
2
+
2.00
0
+
2.15 1.74 0.717
+ 1 + 0 1 3 + +
0
+
Be
10
1.60
C3
10
T 3 1 =
T=1
B
10
T=03
vo t (r-r ) o o
t=0
1111111111111111 0000000000000000 1111111111111111 0000000000000000 1111111111111111 0000000000000000 1111111111111111 0000000000000000ko
111 000 111 000 111 000 111 000 111 000 111 000
z
t>0
1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 r 1111111111111111111111111111111 0000000000000000000000000000000 o (r-vo t-ro ) 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 111 000 1111111111111111111111111111111 0000000000000000000000000000000 111 000 111111111111111 000000000000000 111 000 1111111111111111111111111111111 0000000000000000000000000000000 z 111 000 111111111111111 000000000000000 111 000 1111111111111111111111111111111 0000000000000000000000000000000 111 000 111111111111111 000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 111111111111111 000000000000000 V(r) 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 (ko r-vo t-r o ) f (r) 1111111111111111111111111111111 0000000000000000000000000000000 o 1111111111111111111111111111111 0000000000000000000000000000000 r 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000 1111111111111111111111111111111 0000000000000000000000000000000+
V(r)
ko
E me c 2 + 1/2 2 + 1/2 1 + 3/2 1 1/2 2 + 3/2 0 1/2 1 + 5/2 0 3/2 1
me c 2
(1 Z 2 )
2 2
+ 1/2 0 l~0
l~1
l~2
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