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E
hm
L
L
n
L
n
L
nn
nx ny
x
x
y
y
xy
,
22
2
2
2
2
2
8
1
4
=+
F
H
G
I
K
J
F
H
G
I
K
J
and the corresponding differences.
(a) For
n
x
=
n
y
= 1, the ratio becomes
11
2
5
1
4
+
=
..
(b) For
n
x
= 1 and
n
y
= 2, the ratio becomes
14
2
0
0
1
4
+
=
b
g
.
. One can check (by computing
other (
n
x
, n
y
) values) that this is the next to lowest energy in the system.
(c) The lowest set of states that are degenerate are (
n
x
, n
y
) = (1, 4) and (2, 2). Both of
these states have that ratio equal to
6
5
0
0
1
4
+
=
b
g
(d) For
n
x
= 1 and
n
y
= 3, the ratio becomes
19
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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