1. Consider 100 photons diffracting through a thin slit to form a diffraction pattern. If we detect five of the photons in a certain region in the pattern, what is the probability (between 0 and 1) of detecting a photon in this region?

Question

2. Suppose that you open a second identical slit and that the diffraction pattern is one of bright and dark bands. Suppose the region where five photons hit before now has none. A wave theory says that waves that hit before are now canceled by waves from the other slit—that crests and troughs combine to zero. But our measurement is of photons that either make a hit or don’t. How does quantum mechanics reconcile this?

Accepted Answer

1. We have approximately a 0.05 probability of detecting a photon at this location. In quantum mechanics we say [latex]|\psi|^{2} \approx 0.05[/latex]. The true probability could be somewhat more or less than 0.05. Put the other way around, if the true probability is 0.05, then the number of photons detected could be somewhat more or less than 5.

2. Quantum mechanics says that photons propagate as waves and are absorbed as particles, with the probability of absorption governed by the maxima and minima of wave interference. Where the combined wave from the two slits has zero amplitude, the probability of a particle being absorbed is zero.

Question 15.S&C.6: 1. Consider 100 photons diffracting through a thin slit to f...

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