p40_015.pdf

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Chapter 40 - 40.15
15. (a) The allowed energy values are given by E n = n 2 h 2 / 8 mL 2 . The difference in energy between the
state n and the state n +1is
∆ E adj = E n +1 −
E n = ( n +1) 2
−
n 2
8 mL 2 = (2 n +1) h 2
8 mL 2
and
= (2 n +1) h 2
8 mL 2
8 mL 2
n 2 h 2
= 2 n +1
n 2
∆ E adj
E
.
2 n/n 2 =2 /n .
(b) As n −→ ∞ , ∆ E adj and E do not approach 0, but ∆ E adj /E does.
(c) See part (b).
(d) See part (b).
(e) ∆ E adj /E is a better measure than either ∆ E adj or E alone of the extent to which the quantum
result is approximated by the classical result.
−→
2 n and (2 n +1) /n 2
−→
h 2
As n becomes large, 2 n +1
 

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