The behavior of photons in the double-slit experiment can indeed be puzzling when considering their dual nature as both particles and waves. Let's break it down to address your question.
In the double-slit experiment with photons, each individual photon behaves as an independent particle that can be detected at a specific point on the screen. However, the pattern that emerges over time, as more and more photons are detected, forms an interference pattern characteristic of wave-like behavior.
This apparent contradiction is resolved by understanding that the wave-like behavior arises from the probabilistic nature of quantum mechanics. Before a measurement is made, a photon exists in a superposition of all possible states, including passing through both slits simultaneously. The wavefunction of the photon describes the probability amplitude for it to be detected at different positions on the screen.
When many photons are sent through the double slits, their individual wavefunctions combine and interfere with each other, resulting in the observed interference pattern. This interference occurs because the probabilities associated with different paths through the slits add up or cancel out, leading to constructive or destructive interference at different positions on the screen.
However, when a measurement is made to determine which slit the photon passes through, its wavefunction "collapses" into a single well-defined state corresponding to passing through a specific slit. This collapses the wave-like behavior and destroys the interference pattern, as now the photon is behaving more like a particle with a definite position.
So, in summary, each photon is indeed detected as an individual particle at a specific location on the screen, but the accumulation of many photons exhibits wave-like interference patterns due to the probabilistic nature of quantum mechanics and the superposition of their wavefunctions. The behavior of photons in the double-slit experiment reflects the wave-particle duality inherent in quantum mechanics.