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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Physics, 2m, Ly, 11 inch

Click to edit the document details