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30. In analogy to Eq. 3910, the normalized wave function in two dimensions can be
written as
,
22
(, )
() ()
s
i
n
s
i
n
4
sin
sin
.
xy
x
y
y
x
nn
n
n
xx
yy
y
x
x
y
n
n
x
yx
y
x
y
LL
n
n
L
L
π
ψ
ψψ
⎛⎞
==
⋅
⎜⎟
⎝⎠
=
The probability of detection by a probe of dimension
x y
∆ ∆
placed at ( , )
x y
is
2
,
4(
)
s
i
n
s
i
n
.
y
x
x
y
n
n
pxy
x
y
L
L
∆∆
=∆
∆
=
A detection probability of 0.0450 of a groundstate electron (
1
=
=
) by a probe of
area
2
400 pm
∆∆ =
placed at ( , )
( /8, /8)
L
L
=
implies
2
2
4
2
4(400 pm )
20 pm
0.0450
sin
sin
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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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