In the double-slit experiment with single electrons, the behavior of individual electrons is described by a probability wave or wavefunction, as described by quantum mechanics. This wavefunction gives the probability distribution of finding the electron at different locations.
In the double-slit experiment, electrons are typically emitted one at a time, and they exhibit wave-like interference patterns on the screen behind the slits. The interference pattern arises because the electron's wavefunction passes through both slits and interferes with itself, creating regions of constructive and destructive interference on the screen.
According to quantum mechanics, the wavefunction does not represent the exact position of the electron but rather a probability distribution. This means that there is a non-zero probability of the electron appearing at any location in the universe, including locations far away from the screen. However, the probability of finding the electron decreases rapidly as we move away from the region of interest, which is near the double slits and the screen.
So, in the case of the double-slit experiment with single electrons, not every electron will necessarily "hit" the screen. Some electrons will be detected on the screen, contributing to the observed interference pattern, while others may be detected elsewhere or not detected at all. The exact position of each electron is not determined until a measurement is made. Before measurement, the electron's behavior is described by the probabilistic nature of the wavefunction.
It's important to note that the wavefunction collapse, which occurs upon measurement, determines the specific outcome and localizes the electron to a particular position. Until then, the electron's position is described by the probability distribution given by the wavefunction.