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µ
( ) ( ) ( ) ( ) ( )
2
1
(1.1)
2
j
j k j k j k
H r V r r E k r
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Ψ = − ∇ + Ψ = Ψ
r r r
r r r r r
!
( ) ( )
( )
1.2
ik R
j k j k
r R e rΨ + = Ψ
r ur
r r
r ur r
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1.3
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k
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m
δ
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1.5
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0
Ω
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k
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1.7
k k
k k k
I r V r r dr
r V r G r r V r r drdr
Ω
Ω Ω
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′ ′ ′ ′
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∫ ∫
r r
r r r
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r r r r r r r r
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ij
k ik jk
ik k jk
I r V r r dr
r V r G r r r drdr
ϕ ϕ
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∫
∫ ∫
r r r
r r r
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k
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r
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k
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r
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ik
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r
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ik
C
δ
r
i
I
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ij
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( )
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ij
k jk
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jk
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r
ij
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ij
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0
1
1.16
j j
j
j
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′ ′
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r r r r
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k
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0
ˆ
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0
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( )
j
rΨ
r
Ω
( )
( )
1
i k K r
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+
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r
r
r
r
r
r
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( )
( )
( )
( )
2
1
1.18
2
i k K r r
k
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m
′
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r
r
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r r
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3
1 3 3 2
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2
3
1.19
2
K K
k
K
V K K V K K
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k K
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m
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÷
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+
÷
−
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r r
r
r
r r r r
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r
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r
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I
0
r
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r r
′
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ω
′
0
r
ε
−
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0
ε
→
0
ε
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4'P*
( ) ( ) ( )
2
1
2
V r r E r
m
Ψ = ∇ + Ψ
÷
r r r
"V
7*
( ) ( ) ( ) ( ) ( )
2
1
2
G r r V r r dr G r r E r dr
m
ω ω
′ ′
′ ′
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÷
∫ ∫
r r r r r r r r r
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( ) ( ) ( ) ( )
( )
( )
( )
( )
2 2
1 1
2 2
1
2
S
G r r E r dr r E G r r dr
m m
r G r r
G r r r dS
m r r
ω ω
′ ′
′
′ ′
− ∇ + Ψ = Ψ ∇ + − +
÷ ÷
′
∂Ψ ∂ −
′
+ − − Ψ
∂ ∂
∫ ∫
∫
r r r r r r r r
r r r
r r r
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( )
0
r
ε
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r
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( )
( )
( )
( )
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1
1.21
2
S
r G r r V r r dr
r G r r
G r r r dS
m r r
ω
′
′
′ ′
Ψ − − Ψ =
′
∂Ψ ∂ −
′
= − − − Ψ
∂ ∂
∫
∫
r r r r r r
r r r
r r r
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*+%8%':*
( )
V r
r
0
r
( ) ( ) ( ) ( ) ( ) ( )
0
0
limG r r V r r dr G r r V r r dr
ε
ω
→
′
Ω
′ ′
− Ψ = − Ψ
∫ ∫
r r r r r r r r r r
"f
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0
ε
→
( )
( )
( )
( )
( )
0 1.22
S
r G r r
G r r r dS
r r
′
′
∂Ψ ∂ −
′
− − Ψ =
∂ ∂
∫
r r r
r r r
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c%&I"!"J':*
I
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
0 0 0
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1
2
S
I r V r r G r r V r r dr dr r V r
m
r G r r
G r r r dS dr
r r
Ω Ω Ω
′
′ ′ ′ ′
= Ψ Ψ − − Ψ = − Ψ ×
′ ′
∂Ψ ∂ −
′ ′ ′
× − − Ψ
′ ′
∂ ∂
∫ ∫ ∫
∫
r r r r r r r r r r r
r r r
r r r r
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0
Ω
ω
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ε
−
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( )
( )
( ) ( )
( )
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*
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1
2
1
2
S
r V r G r r dr G r r E r dr
m
r G r r
r G r r r dS
m r r
ω ω
′′ ′′
′′
′ ′
Ψ − = − ∇ + Ψ
÷
′
∂Ψ ∂ −
′ ′
= Ψ + − − Ψ
∂ ∂
∫ ∫
∫
r r r r r r r r r
r r r
r r r r
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2r
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−
I
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( )
( )
( )
( ) ( )
*
*
2
0
1
lim
4
1.23
S S
r
I dS dS r
m r r
r
r G r r
r r
ε
→
′′ ′
∂Ψ
∂
′
= − Ψ ×
∂ ∂
′
∂Ψ
∂
′ ′
× Ψ − −
′ ′
∂ ∂
∫ ∫
r
r
r
r r r
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lm l
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k k
H r E r
ψ ψ
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r r
µ
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2
H V r
m
∇
= − +
r
h
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r
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r
µ
0
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ψ ψ
=
r r
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µ
2
2
0
0
( ) (2.4)
2
H V r
m
= − ∇ +
r
h
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0
(2.5)H H W= +
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W
∧
µ
0
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r r
!M
0
( ) ( ) (2.7)
n n
k
n
r C r R
ψ ψ
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r
r r uur
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r R−
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r R
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r uur
n
n
r R−
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r
r
n
R
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