Midterm 1 Solutions
2/26/2010
1.
(a) Answer:
iii and vii
See problem set 3 question 2.b).
Scoring:
7
x

3
.
5
y
, where
x
are the number of correct answers and
y
are the
number of incorrect answers. Note that negative scores were treated as 0.
(b) Answer:
ii and v
See problem set 3 question 2.b).
Notice that multiplying a wave function by
i
does
not
change the wave function.
Scoring:
7
x

4
y
(c) Answer:
ii, iv, and vi Remember that for any operator we have,
d
h
ˆ
G
i
dt
=
1
i
~
h
[
ˆ
G,
H
]
i
This equation was given to you at the beginning of the exam.
Of course,
H
commutes with itself and so its expectation value is timeindependent.
You can calculate the uncertainty in
H
which is
K
.
Problem set 3 question 2.c) provides the final answer.
Scoring:
6
x

6
y
(d) Answer:
iii, iv, v, and vii

A
i
and

B
i
are orthonormal and the action of
ˆ
C
on both states is given. Using
this information you can show that iii and iv are true.
You know the action of
ˆ
C
and
H
on both

A
i
and

B
i
so you can create the
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 Spring '10
 DAVIDCHANDLER
 Fundamental physics concepts, virial theorem, true. n+ mω

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