71. For U = U
0
, Schr¨
odinger’s equation becomes
d
2
ψ
dx
2
+
8π
2
m
h
2
[E
− U
0
] ψ = 0 .
We substitute ψ = ψ
0
e
ikx
. The second derivative is d
2
ψ/dx
2
=
−k
2
ψ
0
e
ikx
=
−k
2
ψ. The result is
−k
2
ψ +
8π
2
m
h
2
[E
− U
0
] ψ = 0 .
Solving for k, we obtain
k =
8π
2
m
h
2
[E
− U
0
] =
2π
h
2m [E
− U
0
] .