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The double-slit experiment is a classic experiment in quantum mechanics that demonstrates the wave-particle duality of particles. It shows that even when particles are sent through the experiment one at a time, they still exhibit wave-like behavior, leading to an interference pattern on the detection screen.

Here's a simplified explanation of how the double-slit experiment works with one particle at a time:

  1. Experimental Setup: A screen with two slits is placed in front of a detection screen, and a particle source, such as an electron gun or photon source, is set up to emit particles one at a time. The particles pass through the slits and then interact with the detection screen.

  2. Wave-like Propagation: When a particle is emitted from the source, it has certain properties associated with it, such as position and momentum. According to quantum mechanics, these properties are described by wavefunctions, which determine the probability distribution of where the particle is likely to be detected.

  3. Interference Pattern: As the particle passes through the slits, its wavefunction spreads out and interacts with itself. This interaction leads to an interference pattern on the detection screen, where some areas experience constructive interference (peaks) and others experience destructive interference (troughs).

  4. Accumulation of Particle Hits: By sending particles one at a time through the double slits and detecting their positions on the screen, we observe that over time, the particles collectively create an interference pattern. This pattern emerges as the individual particle hits accumulate, demonstrating wave-like behavior.

The key concept here is that even when particles are sent through the experiment one at a time, their wavefunctions interfere with themselves, leading to an interference pattern. This phenomenon arises because particles exhibit both particle-like and wave-like characteristics, and their behavior is described by wavefunctions that can interfere with each other.

The double-slit experiment with one particle at a time highlights the probabilistic nature of quantum mechanics and the inherent wave-particle duality of particles. It demonstrates that particles, even when treated as discrete entities, can exhibit wave-like properties and interference effects, challenging our classical intuitions about the behavior of objects.

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