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26. We are looking for the values of the ratio
E
nx,ny
h
2
/
8
mL
2
=
L
2
Ã
n
2
x
L
2
x
+
n
2
y
L
2
y
!
=
µ
n
2
x
+
1
4
n
2
y
¶
and the corresponding diFerences.
(a) ±or
n
x
=
n
y
=1
,
the ratio becomes 1 +
1
4
=1
.
25.
(b) ±or
n
x
=1and
n
y
=2
,
the ratio becomes 1 +
1
4
(4) = 2
.
00. 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 1 +
1
4
(16) = 5
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 Fall '08
 SPRUNGER
 Physics

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