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C
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c−i∞
1
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t
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t
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1
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7%)4%
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2a2
π
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∞
e
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r
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e 4a .
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<-,
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=8#-
Z
D+
−
Z
D−
1
eλ(− 4a −W ) dt
dW.
t
dW
√
1
i
dt
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2a 2
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√
1
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t
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1 dt
t dW
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1
1
1
4a2 i
1 dt
− 21
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t dW
2a 2
1
1
1
1
3
3
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I(λ) ∼
Z
+
∞
0
Z
∞
0
1
1
− 21
1
2
1
λ
1
2a 2 ie− 4
2πi
1
3
1
2
3
2
3
e−λW (W − 2 − 2ia 2 − 4aW 2 + 8ia 2 W + 16a2 W 2 + . . . ) dW
e
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2
3
2
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λ 5
Γ( 32 )
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2 Γ( 2 )
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5
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λ2
λ2
λ2
r
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λ
λ
1
2
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Z
∞
−∞
3
eiλ(t+t /3)
dt.
2t2 + 1
+,-./
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p(±i) = ∓2/3,
p′′ (±i) = ∓2.
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eiλ(t+t
3 /3)
∼ O(e−
λR3
3
sin(3φ)
)
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(" 72! 955!*@2$6: 56$"! 72! #'"7'9* %2'96) A!<(" $") !") (" 72! %!#7'*%
2π/3 < φ < π, $") 0 < φ < π/3.
82! %7!!5!%7 )!%#!"7B$%#!"7 5$72% %$7(%:>
<(3("< 1(72 t = x + iy=
ℑ(p(t)) = ℑ(p(±i)) = 0
1
x2
ℑ[i(x + iy + (x3 + 3ix2 y − 3xy 2 − iy 3 ))] = x(1 +
− y 2 ).
3
3
?' 72! %7!!5!%7 )!%#!"7 5$72% !4$"$7("< :*'4 t = i $*! 1 + x3 − y2 = 0 $") :*'4
t = −i $*! x = 00'7! $6%' 72$7 (: y2 = ( x3 − 1) 72!" :'* 6$*<! x 1! 2$3! y ∼ ± √13 x- C %D!7#2
': 72! 5$72 (% <(3!" (" E<- ,82! $A'3! $"$6>%(% %9<<!%7% 72$7 1! #$" )!:'*4 72! '*(<("$6 #'"7'9* (" +,-./
7' 72! 955!*@2$6: 56$"! '" 7' 72! %7!!5!%7 )!#%!"7 5$72 72*'9<2 t = i= %!! E<- ,C556>("< &$9#2>F% 72!'*!4 1! 'A7$("
2
2
Z
√
eiλ(t+t /3)
2],
dt
=
2πiRes[t
=
i/
2t2 + 1
3
L1 +C1 +C2 +C3
GH
(b)
(a)
y
i
C2
i
C3
C1
L1
x
−i
!"#$% &' ()* +,%%-%., /%.0%1, -),2 ,2$3#"2
36 5)#0289. ,2%3$%:;
.!10% ,2% !1,%"$)1/ 2). ) .!:-7% -37% ),
"3%. ,3 =%$3 63$ 7)$"% R )1/ .3
Z
3
L1
eiλ(t+t /3)
dt =
2t2 + 1
Z
(4* 531,3#$. 63$ )--7!0),!31
√
t = i/ 2.
3
−C2
t=i
<2% !1,%"$)7. )731"
eiλ(t+t /3)
e
dt
+
2πi[
2t2 + 1
iλ( √i −
2
4i
√
2
6
C 1 , C3
i
√
)
2
].
3$ ,2% !1,%"$)7 )731" ,2% .,%%-%., /%.0%1, -),2 >% 0)1 -#, (63$ ,2% 7%)/!1" 3$/%$
031,$!4#,!31 3178* t = i + T ,3 34,)!1
√
2
2
2 − 5λ
eλ(− 3 −T )
√
dT +
πe 6 2 ,
I(λ) ∼
2
−∞ (−2 + 1)
√
r
π −2λ/3
2 − 5λ
√
e
+
πe 6 2 .
∼−
λ
2
Z
∞
??