PHY662, Spring 2004, Feb. 10, 2004
24th February 2004
1 Miscellaneous
1. HWK #7 is due Tues., Mar. 2.
2. I am out of town on Mon., Mar. 1 - so I encourage you to start early on the
homework.
3. Continue to read Ch. 17 Shankar (or Griffiths Ch. 6).
4. Today: HWK #6 key, WKB wrap-up, tunneling, intro to perturbation theory in
physics, maybe start non-degenerate time-independent perturbation theory.
2 Homework #6 review.
3 WKB - a little more.
1. The expansion condition is k0k2. This is the same as d
dx (ln k)< k: the
fractional rate of change of kis small over one wavelength (λ=2π
k).
2. The trickiest part of the WKB approximation is where the classical momentum
vanishes. This is where the oscillating solution needs to be connected to the
exponential solution. Leads to connection functions:
(a) These are simple if the potential changes very rapidly (over a distance much
less than the particle “wavelength”). Apply continuity or vanishing of the
wave function.
(b) Example: quantization condition in a well with sharp sides gives 2Rx2
x1dx p2m(E−V) =
nh. [come back to after Merzbacher].
(c) Otherwise, need to be careful, use connection formula. These give, for
example, the quantization condition 2Rx2
x1dx p2m(E−V) = (n+1
2)h
for a bound state with classical turning points x1and x2.
3. Griffith’s example of tunneling through a large sharp barrier.
4. Discuss tunneling out of a box.
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