1549380323-Statistical Mechanics Theory and Molecular Simulation

448 The Feynman path integral

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Fig. 12.2Interference pattern expected for classical electrons impinging on the double-slit
apparatus.

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.y

Fig. 12.3Illustration of possible paths of quantum electrons through a double-slit apparatus.

P(y) =|A 1 (y)|^2 +|A 2 (y)|^2 + 2|A 1 (y)||A 2 (y)|cos (φ 1 (y)−φ 2 (y)). (12.1.2)

The third term in eqn. (12.1.2) is the interference term between thetwo paths, and the
expression forP(y) gives us our first clue that this term, which contains an oscillating
function of the phase difference multiplied by an amplitude|A 1 (y)||A 2 (y)|, is largely
responsible for the overall shape of the observed interference pattern.