p40_015 - 15(a The allowed energy values are given by En =...

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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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