In the double-slit experiment performed with single photons, the behavior of the photons can be described in terms of wave-particle duality. Each individual photon can exhibit wave-like behavior and interfere with itself, leading to an interference pattern on the screen. However, it is important to note that this does not mean the photon exists in two places at the same time in a classical sense.
When a single photon is sent through the double-slit apparatus, it is prepared in a quantum superposition of possible states. This superposition includes all the possible paths the photon could take, including going through both slits simultaneously. The wave function, which describes the probability distribution of the photon, evolves and interferes with itself, resulting in an interference pattern on the screen.
However, when the photon is detected on the screen, it is always detected as a single particle at a specific location. The act of detection "collapses" the photon's wave function, forcing it into a definite state. At the point of detection, the photon is localized to a particular position on the screen, and the interference pattern is no longer observed.
So, while it is mathematically accurate to describe the photon's behavior in terms of a superposition of states and interference, it is not correct to say that the photon exists in two places at the same time or that it interacts with itself in a classical sense. The wave-like behavior and interference effects arise from the probabilistic nature of quantum mechanics and the wave-particle duality exhibited by particles at the quantum level.