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  {\bf University of Kentucky, Physics 520 \\
    Homework \#2, Rev. B, due Friday, 2015-09-09 }
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{\bf 0.} Griffiths [2ed]
Ch.~1 \#11, %p20, speedometer needle
      \#12, %p21,  " projection
      \#13. %p21, Buffon's needle

{\bf 1. Bohr's Oscillator.}  A 3-dimensional ideal frictionless harmonic
oscillator of mass $m$ and natural angular frequency $\omega$ is similar to a
hydrogen atom, except instead of $F=Ze^2/4\pi\epsilon_0 r^2$, the central force
is $F=kr$ with spring constant $k=m\omega^2$.

{\bf \quad a)} In the same way that Bohr quantized the hydrogen atom, use
quantization of angular momentum $L=\hbar n$ to calculate the radius $r_n$,
velocity $v_n$, and energy levels $E_n$ of the stationary orbits (states) of
the harmonic oscillator.

{\bf \quad b)} Calculate spectrum of emitted wavelengths.

{\bf \quad c)} Show that Bohr's correspondence principle holds for this system.

{\bf 2. Surface optics.}  Use the principle of constructive interference to
show that one single formula $\Delta(nd\sin\theta)\equiv
(n_2\sin\theta_2-n_1\sin\theta_1) d = m \lambda$ applies to reflection,
refraction, and diffraction at the interface between two media with indices of
refraction $n_1$ and $n_2$. $\theta_{1,2}$ are the angles of the incident and
outgoing waves, respectively, measure from the normal.  $d$ is the spacing
between individual rules of the diffraction grating, which are perpendicular
to the plane of incidence, and $m$ is the order of diffraction.  Note that
diffraction can be either reflective or transmissive, with the
0$^{\mathrm{th}}$ order diffraction peak corresponding to reflection or
refraction, respectively, in which case $d$ is irrelevant.

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