PHYS 408 HOMEWORK 6 SOLUTIONS

# B2 kb 2 exp i kd cos x 4 d 2d d dkx ei 2 k2 kx d

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Unformatted text preview: ￿ ￿￿ 1 2π k kx2 exp i kd + − π /4 |α| d 2d (67) (68) (69) The wave fronts are parabolic, i.e. d ∝ x2 . Compare this problem to the f (x, y ) = δ (x)δ (y ) discussed in class. Note that (at least in my opinion) accurate intuition for a delta-function slit is more diﬃcult to attain than that for a slit of ﬁnite (but arbitrary) width, in large part because the delta function model leads expressions that are not as easy to handle analytically or numerically. 11 11.4 two delta-function slits, relative phase diﬀerence f (x, y ) = δ (x − b) + iδ (x + b) (70) ￿ ￿ ˜ f (kx , ky ) = e−ikx b + ie+ikx b δ (ky ) g (x, y ) = = = = ≈ = = ￿ ￿ ￿ dkx dkx ￿ ￿ dky ei √ dky ei √ √ 2 2 k2 −kx −ky d i(kx x+ky y ) e 2 2 k2 −kx −ky d i(kx x+ky y ) e ￿ ￿ e−ikx b + ie+ikx b δ (ky ) ￿ e−ikx b + ie+ikx b δ (ky ) ￿ e−ikx b + ie+ikx b ￿ ￿ √ √2 2 2 i k2 −kx d ikx (x−b) iπ /2 dkx e e +e dkx ei k −kx d eikx (x+b) ￿ ￿ ￿ 1 2π k...
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