PHY 4604 Fall 2010 – Homework 5
Due by 5:00 p.m. on Monday, November 1. Please deliver your homework to
NPB 2162, or push it under the door if the room is unoccupied.
No credit will be
available for homework submitted after the start of class on Friday, November 5.
Answer both 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.
1.
Half potentials.
Any potential
V
s
(
x
) that is mirror symmetric about
x
= 0, i.e.,
V
s
(

x
)=
V
s
(
x
) for all
x
has
N
s
bound states labeled
n
=0
,1
,2
,
... , N
s

1w
i
th
energies
E
s,n
that satisfy
E
s,n
+1
>E
s,n
and with normalized wave functions
ψ
s,n
(
x
)
that satisfy
ψ
s,n
(

x
)=(

1)
n
ψ
s,n
(
x
).
Then the “half potential”
V
h
(
x
) formed from
V
s
(
x
) by inserting a hard wall that pre
vents the particle entering the region
x<
0, i.e.,
V
h
(
x
)=
(
V
s
(
x
)
for
x>
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, Hilbert space, normalized wave functions, state vector, Ns bound states, corresponding normalized eigenstates

Click to edit the document details