5.20: Electron Diffraction at Multiple Slits

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The American Journal of Physics published a translation of Claus Jonsson's paper "Electron Diffraction at Multiple Slits" in American Journal of Physics 42, 4-11 (1974). The following calculations are in agreement with the diffraction patterns reported by Jonsson.

\[ \begin{matrix} \text{Number of slits:} & n = 6 & \text{Slit width:} & w = .5 \\ \text{Slit locations:} & s_1 = 0 & s_2 = 2 & s_3 = 4 & s_4 = 6 & s_5 = 8 & s_6 = 10 \end{matrix} \nonumber \]

Normalized coordinate-space wave function at the slit screen:

\[ \Psi (x) = \frac{1}{ \sqrt{N}} \left| \begin{matrix} \frac{1}{ \sqrt{w}} \text{ if } \sum_{j = 1}^{n} \left[ ( x \geq - s_j ) ( x \leq s_j + w ) \right] \\ 0 \text{otherwise} \end{matrix} \right. \nonumber \]

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Fourier transform the position wave function into the momentum representation:

\[ \Phi (p_x) = \frac{1}{ \sqrt{2 \pi}} \int_0 ^{s_n + w} exp(-i p_x x) \Psi (x) dx \nonumber \]

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