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17. The probability that the electron is found in any interval is given by
P
=
R

ψ

2
dx
, where the integral is
over the interval. If the interval width ∆
x
is small, the probability can be approximated by
P
=

ψ

2
∆
x
,
where the wave function is evaluated for the center of the interval, say. For an electron trapped in an
in±nite well of width
L
, the ground state probability density is

ψ

2
=
2
L
sin
2
³
πx
L
´
,
so
P
=
µ
2∆
x
L
¶
sin
2
³
πx
L
´
.
(a) We take
L
= 100 pm,
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 Fall '08
 SPRUNGER
 Physics

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