CH202 Study Guide - Final Guide: Photographic Plate, Normal Distribution, Electron Gun
Two-slit interference
An imaginary experiment will clarify the physical implications of
the prin- ciple and suggest how it might be tested
experimentally. The apparatus consists of an electron gun, G, a
screen with two narrow slits S1 and S2, and a photographic plate
P, which darkens when hit by an electron (see Figure 1.1).
When an electron is emitted by G, it has an amplitude to pass
through slit S1 and then hit the screen at the point x. This
amplitude will clearly depend on the point x, so we label it A1(x).
Similarly, there is an amplitude A2(x) that the electron passed
through S2 before reaching the screen at x. Hence the
probability that the electron arrives at x is
P(x) = |A1(x) + A2(x)|2 = |A1(x)|2 + |A2(x)|2 + 2Re(A1(x)A∗2(x)).
(1.13)
|A1(x)|2 is simply the probability that the electron reaches the
plate after passing through S1. We expect this to be a roughly
Gaussian distribution p1(x) that is centred on the value x1 of x at
which a straight line from G through the middle of S1 hits the
plate. |A2(x)|2 should similarly be a roughly Gaussian function
p2(x) centred on the intersection at x2 of the screen and the
straight line from G through the middle of S2. It is convenient to
write
Ai = |Ai|eiφi = √
pieiφi, where φi is the phase of the complex number Ai.
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