This preview shows page 1. Sign up to view the full content.
58. (a) and (b) In the region 0 <
x
<
L
,
U
0
= 0, so Schrödinger’s equation for the region is
d
dx
m
h
E
2
2
2
2
8
0
ψ
+=
π
where
E
> 0. If
2
(
x
) =
B
sin
2
kx
, then
(
x
) =
B'
sin
kx
, where
B'
is another constant
satisfying
B'
2
=
B
. Thus,
2
22
2
sin
( )
d
kB
k
x
k
x
dx
′
=−
and
d
dx
m
h
Ek
m
h
E
2
2
2
2
2
2
2
88
ψψ
−
+
ππ
.
This is zero provided that
k
mE
h
2
2
2
8
=
π
The quantity on the righthand side is positive, so
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

Click to edit the document details