This preview shows pages 1–2. Sign up to view the full content.
PHY 4604 Fall 2010 – Homework 3
Due at the start of class on Friday, October 1.
No credit will be available for homework
submitted after the start of class on Monday, October 4.
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.
Note: It is possible to fully answer all the questions without performing any integration.
1. For a particle of mass
m
moving in the potential
V
(
x
)=
1
2
mω
2
x
2
, it is often convenient
to express the position and momentum operators in terms of the ladder operators
a
±
:
x
=
r
~
2
mω
(
a
+
+
a

)
,p
=
i
r
~
mω
2
(
a
+

a

)
.
(a) Evaluate
h
x
i
,
h
x
2
i
,
σ
x
,
h
p
i
,
h
p
2
i
,and
σ
p
for the stationary state
ψ
n
(where
n
=0
is the ground state). Check whether the uncertainty principle is obeyed.
(b) Evaluate
h
x
i
,
h
x
2
i
,
σ
x
,
h
p
i
,
h
p
2
i
σ
p
at time
t>
0 for the state Ψ(
x, t
)that
starts out as Ψ(
x,
0) = [4
ψ
0
(
x
)+3
iψ
1
(
x
)]
/
5.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 Field
 mechanics, Work

Click to edit the document details