Preliminary Test, (
Answers
)
Question 1
st
:
Method 1
st
:
It could be noticed that in the previous studies we got familiar with another simpler
example of 1D rigid box problem: you have a 1D rigid box whose two boundaries are
located at x=0 and x=a, then you know the wave function of the particle confined in
this box is (in which n are any positive integers):
(
29
2
sin
0
0
0
n
n x
x
a
x
a
a
x
or x
a
π
ψ
<
<
÷
=
<
.
Now the question is similar, differing from the above case only in that the rigid box
now is located at
x
L
= ±
. So you can use the results of the above case directly, with
some mathematical transformation:
Set
y
x
L
=
+
, and we have
[
]
0,2
y
L
∈
as a new variable, and thus this question is
changed into follows: a particle is confined in a rigid box located at
[
]
0,2
y
L
∈
. So
simply using the above result you know that the wave function in our question can be
written as:
(
29
2
sin
0
2
2
2
0
0
2
n
n y
y
L
y
L
L
y
or y
L
<
<
÷
=
<
.
Changing this result back into x we obtain:
(
29
(
29
2
sin
0
2
2
2
0
0
2
n
n
x
L
x
L
L
y
L
L
L
x
L
or x
L
L
+
<
+
<
÷

=
+
<
+
.
This is, of course, equivalent to the following and our final result:
(
29
(
29
1
sin
2
0
n
n
x
L
L
x
L
x
L
L
x
L or x
L
+

<
<
÷
=
.
Method 2
nd
:
You may also use the ordinary method as you do in any other cases, that is, solving
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.
 Spring '11
 CFLO
 mechanics

Click to edit the document details