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The probability of detection by a probe of dimension
x y
∆ ∆
placed at ( , )
x y
is
2
22
,
4(
)
(, )
s
i
n
s
i
n
.
xy
y
x
nn
x
y
n
n
pxy
x
y
LL
L
L
π
ψ
⎛⎞
∆∆
=∆
∆
=
⎜⎟
⎝⎠
With
150 pm
LLL
==
=
and
5.00 pm
∆ =∆ =
, the probability of detecting an
electron in (
,
)
(1,3)
=
state by placing a probe at (0.200 , 0.800 )
is
()
(
)
2
2
2
2
2
3
4(
)
4(5.00 pm)
3
sin
sin
sin
0.200
sin
0.800
(150 pm)
5.00 pm
4
sin
0.200
sin
2.40
150 pm
1.4 10 .
y
x
x
y
n
n
p
L
L
L
L
L
L
ππ
−
⋅
=
=×
29. The discussion on the probability of detection for onedimensional case found in
Section 394 can be readily extended to two dimensions. In analogy to Eq. 3910, the
normalized wave function in two dimensions can be written as
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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

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