PHY 4604 Fall 2010 – Homework 1
Due at the start of class on Friday, September 3.
No credit will be available for
homework submitted after the start of class on Wednesday, September 8.
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
sin
2
x dx
=
1
2
(
x

sin
x
cos
x
)
,
Z
∞
0
x
2
n
exp(

x
2
/a
2
)
dx
=
√
π
(2
n
)!
n
!
a
2
2
n
+1
.
In the second equation,
a
is real,
n
is a nonnegative integer, and
n
! =
n
·
(
n

1)! with 0! = 1.
1. A pointlike particle of mass
m
moving in one dimension is confined between hard walls
at
x
= 0 and
x
=
L
. The particle is described by the wave function
Ψ(
x, t
) =
(
A
sin(2
πx/L
) exp(

iEt/
~
)
for 0
≤
x
≤
L,
0
otherwise
.
(1)
Here
L
is a real length, while the constants
A
and
E
may be real, imaginary, or complex.
(a) Find a choice of
A
that normalizes the wave function. What condition must be
satisfied to ensure that
A
is truly a constant, i.e., it is independent of time?
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 Fall '07
 Field
 mechanics, Work, wave function, σx

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