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23. Schr¨
odinger’s equation for the region
x>L
is
d
2
ψ
dx
2
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ
=0
.
If
ψ
=
De
2
kx
,then
d
2
ψ/dx
2
=4
k
2
De
2
kx
=4
k
2
ψ
and
d
2
ψ
dx
2
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ
=4
k
2
ψ
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ.
This is zero provided
k
=
π
h
p
2
m
(
U
0
−
E
)
.
The proposed function satisFes Schr¨
odinger’s equation provided
k
has this value. Since
U
0
is greater
than
E
in the region
x>L
, the quantity under the radical is positive. This means
k
is real. If
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 Fall '08
 SPRUNGER
 Physics

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