p40_026 - 26. We are looking for the values of the ratio n2...

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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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