PHY 4604 Fall 2009 – Homework 3
Due at the start of class on Wednesday, September 30.
No credit will be available
for homework submitted after the start of class on Monday, October 5.
Answer all three questions. Please write neatly and include your name on the front page of
your answers. You must also clearly identify all your collaborators on this assignment. To
gain maximum credit you should explain your reasoning and show all working.
These questions are similar in length and difficulty to those that will appear on the first mid
term exam. The exam will likely consist of one question requiring quantitative calculations
(like question 1 or question 2 below) and one question requiring a more qualitative answer
(like question 3).
Your may find useful the following integrals:
Z
∞
0
x
2
n
e

x
2
dx
=
√
π
(2
n
)!
2
2
n
+1
n
!
Z
∞
0
x
2
n
+1
e

x
2
dx
=
n
!
2
1. Consider a particle of mass
m
oscillating in one dimension at the end of an ideal spring
of spring constant
k
, i.e., having a potential energy
V
(
x
) =
1
2
kx
2
.
Suppose that at
time
t
= 0, this system is in the quantummechanical state (1

2
i
)
ψ
2
(
x
)
/
√
5 (where
ψ
n
with
n
= 0
,
1
,
2
, . . .
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 Fall '07
 Field
 mechanics, Work, π, stationary states, exponential decay length, e−x/l

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