Physics H7C Fall 1999
Solutions to Problem Set 7
Derek Kimball
Above the front door of Niels Bohr’s cottage was nailed a horseshoe. A visitor who
saw it exclaimed: “Being as great a scientist as you are, do you really believe that
a horseshoe above the entrance to a home brings good luck?”
“No,” answered Bohr, “I certainly do not believe in this superstition. But you
know,” he added with a smile, “they say that it does bring luck even if you don’t
believe in it!”
 George Gamow, excerpted from
Thirty Years that Shook Physics
.
If you have any questions, suggestions or corrections to the solutions, don’t hesitate
to email me at [email protected]!
Problem 1
This problem makes sense only if you make some rather poorly motivated ap
proximations. In particular, we must assume that we are far away from resonance
(namely that
ω
2
0
−
ω
2
≫
γω
). We also can assume that there are very few electrons
(namely that
Ne
2
mǫ
0
≪
1, which is wellmotivated by the fact that
κ
is much less than
n
, i.e. few absorbers). If we make these approximations, the results follow almost
immediately. If you don’t make these assumptions, then the results are clearly
incorrect (see Figure 6.1 in Fowles, which is nothing like the equations Fowles asks
us to derive). Thus, we’ll make these assumptions!
Then we can apply these approximations to equations 6.34 and 6.35 in Fowles. We
find that:
n
2
−
κ
2
≈
n
2
≈
1 +
Ne
2
mǫ
0
1
ω
2
0
−
ω
2
(1)
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 Fall '09
 Physics, Normal Distribution, Probability theory, probability density function, order Taylor expansion, Physics H7C Fall

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