p40_021.pdf
(
59 KB
)
Pobierz
Chapter 40 - 40.21
21. (a) and (b) Schrodinger’s equation for the region
x>L
is
d
2
ψ
dx
2
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ
=0
,
U
0
<
0. If
ψ
2
(
x
)=
Ce
−
2
kx
,then
ψ
(
x
)=
C
e
−kx
,where
C
is another constant satisfying
C
2
=
C
.Thus
d
2
ψ/dx
2
=4
k
2
C
e
−kx
=4
k
2
ψ
and
−
d
2
ψ
dx
2
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ
=
k
2
ψ
+
8
π
2
m
h
2
[
E
−
U
0
]
ψ.
This is zero provided that
k
2
=
8
π
2
m
h
2
[
U
0
−
E
]
.
The quantity on the right-hand side is positive, so
k
is real and the proposed function satisfies
Schrodinger’s equation. If
k
is negative, however, the proposed function would be physically unre-
alistic. It would increase exponentially with
x
. Since the integral of the probability density over the
entire
x
axis must be finite,
ψ
diverging as
x
→∞
would be unacceptable. Therefore, we choose
k
=
2
π
h
2
m
(
U
0
−
E
)
>
0
.
where
E
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Inne pliki z tego folderu:
p40_001.pdf
(53 KB)
p40_002.pdf
(51 KB)
p40_003.pdf
(52 KB)
p40_004.pdf
(53 KB)
p40_005.pdf
(56 KB)
Inne foldery tego chomika:
chap01
chap02
chap03
chap04
chap05
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