26. We are looking for the values of the ratio


n2
Enx,ny n2 1
y
= L2 x + = n2 + n2
x y
h2/8mL2 L2 L2 4
x y
and the corresponding differences.
1
(a) For nx = ny =1, the ratio becomes 1 + =1.25.
4
1
(b) For nx =1 and ny =2, the ratio becomes 1 + (4) = 2.00. One can check (by computing other
4
(nx, ny) values) that this is the next to lowest energy in the system.
(c) The lowest set of states that are degenerate are (nx, ny) =(1, 4) and (2, 2). Both of these states
1
have that ratio equal to 1 + (16) = 5.00.
4
1
(d) For nx =1 and ny =3, the ratio becomes 1 + (9) = 3.25. One can check (by computing other
4
(nx, ny) values) that this is the lowest energy greater than that computed in part (b). The next
1
higher energy comes from (nx, ny) =(2, 1) for which the ratio is 4 + (1) = 4.25. The difference
4
between these two values is 4.25 - 3.25 = 1.00.