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Homework Week 3: Due Friday, October 16
Chemistry 110A — 2009
Professor McCurdy
1.
Problem 425 in McQuarrie and Simon – The algebra should be very short and it’s a
good idea to do this one before problem 2.
2.
For the particleinbox, the system is prepared in the state described the time
dependent wave function
"
x
,
t
( )
:
"
x
,
t
( )
=
N
#
1
x
( )
e
$
iE
1
t
/
h
+
2
x
( )
e
$
iE
2
t
/
h
( )
where
"
n
x
( )
=
2
L
sin
n
x
L
$
%
’
(
)
and
E
n
=
n
2
2
h
2
2
mL
2
are the normalized particleinabox
functions and their corresponding energies.
(a)
Find the normalization constant N, and show that it does not depend on time.
(b)
Evaluate the expectation value of the energy
E
.
(c)
Evaluate the expectation value of position
x
to show that it is
x
t
=
L
2
"
16
L
9
2
cos
E
2
"
E
1
h
t
$
%
’
(
)
3.
Problem 426 in McQuarrie and Simon.
Hint:
This one is a little tricky at one point. To get to that point you just differentiate the
integral that defines
x
using the product rule. Remember that time is real when you do
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 Spring '09
 Mccurdy
 Chemistry

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