Ph002a, Fall 2009
Quiz 4
Due: 24 November 2009
Preliminary note: You should be able to do this problem by hand, but you
should feel free to use a calculator, Mathematica, or any other symbolic
manipulation program if you ﬁnd it easier to evaluate integrals or numbers
that way.
Consider a quantummechanical particle of mass
m
in a harmonic potential
V
(
x
) = (1
/
2)
mω
2
x
2
, where
ω
is the oscillator frequency, and the spatial
coordinate
x
spans the range
∞
< x <
∞
. Suppose furthermore that
someone tells you that at some particular time, the spatial part of the wave
function is
ψ
a
(
x
) =
±
A
(
a
2

x
2
)
for

x

< a,
0
,
for

x

> a,
(1)
where
A
is a normalization constant, and
a
is a distance. For reasons that
will become clear below, we will refer to
ψ
a
(
x
) as a “trial wave function”.
Note that
ψ
a
(
x
) is
not
an eigenstate (i.e., it is not a stationary state), but
we will not be considering time evolution so this should not concern you.
1. Calculate the constant
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 Spring '09
 DUDKO
 mechanics, 2m, wave function, expectation value, ea, trial wave

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