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19. Schrödinger’s equation for the region
x
>
L
is
d
dx
m
h
EU
2
2
2
2
0
8
0
ψ
+−
=
π
.
If
=
De
2
kx
, then
d
2
/
dx
2
= 4
k
2
De
2
kx
= 4
k
2
and
d
dx
m
h
k
m
h
2
2
2
2
0
2
2
2
0
8
4
8
ψψ
=
ππ
This is zero provided
k
h
mU
E
=−
π
2
0
bg
The proposed function satisfies Schrödinger’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
k
is positive, however, the proposed function is physically unrealistic.
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 Spring '08
 Any
 Physics

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