Physics 246, Spring 2006
Final Exam
Monday, May 8, 2006
•
Answer all questions, using the paper provided.
Begin each problem on a sepa-
rate sheet.
The pages will be separated for grading, so clearly label the problem
number and put your name on EACH PAGE.
•
One 8.5 by 11 inch cheat sheet (front and back) allowed.
No other books,
calculators or notes allowed.
•
SHOW ALL WORK.
•
This exam has 150 points total.
•
Potentially useful information:
Z
nπ
0
(sin
2
θ
)
dθ
=
Z
nπ
0
(cos
2
θ
)
dθ
=
nπ
2
Z
+
∞
-∞
e
ix
(
k
-
k
0
)
dx
= 2
π δ
(
k
-
k
0
)
ˆ
a
†
|
n >
=
√
n
+ 1
|
n
+ 1
>
ˆ
a
|
n >
=
√
n
|
n
-
1
>
L
±
|
l, m >
= ¯
h
[
l
(
l
+ 1)
-
m
(
m
±
1)]
1
/
2
|
l, m
±
1
>
Z
+
∞
-∞
e
-
y
2
dy
=
√
π
1
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1. Short answer (15 points total). You do not need to explain your answers in this
problem unless explicitly asked to do so.
(a) (2 points)
What are the units of ¯
h
?
(b) (3 points) True or false? In time dependent perturbation theory, a per-
turbation that depends on time can induce transitions between different states
only
if the perturbation also has some space dependence. Explain
briefly
.
(c) (3 points)
For each following operator, state whether it is Hermitian.
i.
x
ii.
∂/∂x
iii. angular momentum raising operator
(d) (2 points)
In matrix mechanics, in a basis of energy eigenstates, what
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- Spring '09
- Physics, 2m, Ly, 11 inch
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