Unformatted text preview: 15. (a) The allowed energy values are given by En = n2 h2 /8mL2 . The diﬀerence in energy between the
state n and the state n + 1 is
∆Eadj = En+1 − En = (n + 1)2 − n2
and ∆Eadj
(2n + 1)h2
=
E
8mL2 8mL2
n2 h2 h2
(2n + 1)h2
=
8mL2
8mL2
= 2n + 1
.
n2 As n becomes large, 2n + 1 −→ 2n and (2n + 1)/n2 −→ 2n/n2 = 2/n.
(b) As n −→ ∞, ∆Eadj and E do not approach 0, but ∆Eadj /E does.
(c) See part (b).
(d) See part (b).
(e) ∆Eadj /E is a better measure than either ∆Eadj or E alone of the extent to which the quantum
result is approximated by the classical result. ...
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 Fall '08
 SPRUNGER
 Physics, Energy

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