Can Two Photons Land in the Same Spot?

Great question! In theory, yes, two photons can land in the exact same spot on the screen, but in practice, this is extremely unlikely due to the nature of the wavefunction probability distribution and quantum mechanics principles.

1. The Wavefunction’s Probability Distribution

• The wavefunction (Ψ) describes a probability amplitude for where each photon could land.
• The square of the wavefunction (|Ψ|²) gives the probability distribution of photon landing spots.
• Since photons arrive one at a time and are independent, each photon’s landing is determined only by this probability distribution, not by where previous photons have landed.

Does the wavefunction allow two photons to land at the exact same point?

• Mathematically, yes—there is a nonzero probability that two or more photons can land at the exact same pixel on the screen.
• However, the probability of this happening is extremely small because of the continuous nature of the probability distribution.

2. Quantum Statistics: Do Photons "Avoid" Each Other?

• Photons are bosons (particles that obey Bose-Einstein statistics).
• Unlike electrons (fermions, which follow the Pauli exclusion principle and avoid each other), bosons actually prefer to cluster.
• This means that if a photon lands in a certain location, the probability of another photon landing in the same location might actually increase slightly (this is called bunching in quantum optics).
• However, since photons are emitted one at a time in the double-slit experiment, this effect is negligible.

3. Experimental Reality: Resolution Limits & Photon Detection

• In actual detectors or photographic plates, the "exact same spot" is defined by pixel size or resolution.
• If two photons land within a few nanometers of each other, they might be registered as the same spot.
• But because the pattern is built over thousands or millions of photons, the statistical distribution dominates.

4. Coherence and Photon Interactions

• If two photons were entangled or otherwise coherent, special interference effects (like Hong-Ou-Mandel interference) could affect their landing probabilities.
• However, in a standard double-slit experiment with single photons, each photon is independent, and their positions on the screen are governed solely by wavefunction probabilities.

Final Answer:

✓ Yes, it is theoretically possible for two photons to land in the exact same spot.
✓ However, in a typical double-slit experiment, this is extremely rare because of the continuous probability distribution.
✓ If measured with finite-resolution detectors, "same spot" means within a small but nonzero area.
✓ Photons, being bosons, don’t repel each other but their individual arrivals are independent in a standard setup.

🚀 Would you like to explore how quantum interference affects multi-photon statistics?

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