ch39-p026 - 26. We are looking for the values of the ratio...

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26. We are looking for the values of the ratio E hm L L n L n L n L nnn x x y y z z xyz ,, 22 2 2 2 2 2 2 2 222 8 =+ + F H G I K J + di and the corresponding differences. (a) For n x = n y = n z = 1, the ratio becomes 1 + 1 + 1 = 3.00. (b) For n x = n y = 2 and n z = 1, the ratio becomes 4 + 4 + 1 = 9.00. One can check (by computing other ( n x , n y , n z ) values) that this is the third lowest energy in the system. One can also check that this same ratio is obtained for ( n x , n y , n z ) = (2, 1, 2) and (1, 2, 2). (c) For n x = n y = 1 and n z = 3, the ratio becomes 1 + 1 + 9 = 11.00. One can check (by computing other ( n x , n y , n z ) values) that this is three “steps” up from the lowest energy in the system. One can also check that this same ratio is obtained for ( n x , n y , n z ) = (1, 3, 1) and (3, 1, 1). If we take the difference between this and the result of part (b), we obtain 11.0 – 9.00 = 2.00. (d) For n x = n y = 1 and n z = 2, the ratio becomes 1 + 1 + 4 = 6.00. One can check (by
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