PHY 4604 Spring 2012 – Homework 1
Due at the start of class on Friday, January 20.
No credit will be available for
homework submitted after the start of class on Wednesday, January 25.
Answer all four 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.
This assignment is primarily designed to provide practice with standard mathematical tech
niques encountered in wave mechanics. You may ﬁnd useful the following integrals:
Z
∞
0
x
2
n
exp(

x
2
/a
2
)
dx
=
√
π
(2
n
)!
n
!
±
a
2
²
2
n
+1
,
Z
∞
0
dx
(
a
2
+
x
2
)
n
+1
=
π
(2
n

1)!!
2
n
+1
a
2
n
+1
n
!
where
a
is real,
n
is a nonnegative integer,
n
!=
n
·
(
n

1)! with 0! = 1, and
n
!! =
n
·
(
n

2)!!
with 0!! = (

1)!! = 1.
1. Consider the wave function
Ψ(
x, t
)=
A
exp[

(
x
2
/
2
a
2
+
iEt/
~
)]
,
(1)
where
a
is a real length scale and
E
isarea
lenergy
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 Spring '07
 Field
 Work, Uncertainty Principle, wave function

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