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13. The probability that the electron is found in any interval is given by
Pd
x
=
z
ψ
2
,
where the integral is over the interval. If the interval width
∆
x
is small, the probability
can be approximated by
P
= 

2
∆
x
, where the wave function is evaluated for the center
of the interval, say. For an electron trapped in an infinite well of width
L
, the ground state
probability density is
2
2
2
=
F
H
G
I
K
J
L
x
L
sin
,
π
so
P
x
L
x
L
=
F
H
G
I
K
J
F
H
G
I
K
J
2
2
∆
.
π
(a) We take
L
= 100 pm,
x
= 25 pm, and
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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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